Tools for Supercritical Carbon Dioxide Cycle Analysis and the Cycle s Applicability to Sodium Fast Reactors

Transcription

1 Tools for Supercritical Carbon Dioxide Cycle Analysis and the Cycle s Applicability to Sodium Fast Reactors By Alexander R. Ludington B.S. Physics United States Naval Academy, 2007 SUBMITTED TO THE DEPARTMENT OF NUCLEAR SCIENCE AND ENGINEERING IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE IN NUCLEAR SCIENCE AND ENGINEERING AT THE MASSACHUSETTS INSTITUTE OF TECHNOLOGY JUNE 2009 Copyright Massachusetts Institute of Technology (MIT) All rights reserved Signature of Author: Department of Nuclear Science and Engineering May 8, 2009 Certified by: Dr. Pavel Hejzlar Thesis Co-Supervisor Principal Research Scientist Certified by: Prof. Michael J. Driscoll Thesis Co-Supervisor Professor Emeritus of Nuclear Science and Engineering Certified by: Prof. Neil E. Todreas Thesis Co-Supervisor Professor Emeritus of Nuclear Science and Engineering Accepted by: Prof. Jacquelyn Yanch Chairman, Department Committee on Graduate Students 1

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3 Tools for Supercritical Carbon Dioxide Cycle Analysis and the Cycle s Applicability to Sodium Fast Reactors By Alexander R. Ludington Submitted to the Department of Nuclear Science and Engineering on May 8, 2009 in partial fulfillment of the requirements for the degree of Master of Science in Nuclear Science and Engineering Abstract The Sodium-Cooled Fast Reactor (SFR) and the Supercritical Carbon Dioxide (S-CO 2 ) Recompression cycle are two technologies that have the potential to impact the power generation landscape of the future. In order for their implementation to be successful, they must compete economically with existing light water reactors and the conventional Rankine cycle. Improvements in efficiency, while maintaining safety and proliferation goals, will allow the SFR to better compete in the electricity generation market. These improvements will depend on core design as well as the balance of plant, including the choice of steam or CO 2 as the working fluid. This work has developed some of the tools necessary for evaluating different design core and balance of plant options. Much of it has concentrated on the S-CO 2 Recompression cycle. S-CO 2 promises to be useful as a working fluid in high-efficiency power conversion systems for SFRs because it achieves higher efficiencies at the high temperatures associated with SFRs. The recompression cycle is capable of operating with very high efficiencies due to the low compressor work needed when CO 2 approaches its critical point at the compressor inlet. The potential of this cycle to meet the needs of next-generation plants must be investigated across the entire range of operations and within each component of the system. A steady-state code for analysis of the recompression cycle was previously developed at MIT in the form of CYCLES II, but the present work has made significant improvements to this code that make the new version, CYCLES III, more versatile. This code can help to size components of the system and predict the costs and performance of the system at steady-state. Coupling of the primary and secondary loops is a major concern, the construction of the intermediate loop and associated heat exchangers (IHX) being critical to cost, efficiency, and safety. Furthermore, there is little experience in industry with large-scale compressors for S-CO 2. The experience that has been gained is typically proprietary. Most existing CO 2 compressors do not operate near the critical point and therefore, perform much like any other semi-ideal gas compressor. Accordingly, consistent, usable models of non-ideal gas compressors have been developed in the present work to produce preliminary designs and performance maps for the compressors in S-CO 2 3

4 recompression cycles. Compressor designs were developed for a 500 MWth S-CO 2 recompression cycle. The main compressor achieves an operating point total-to-static efficiency of 90.4 % and the recompressing compressor achieves 91.4 %. Further work can continue once these areas have been developed, including transient analysis, the effects of impurities on the system, and investigation of cycles which operate on other working fluids. Additionally, changes in the intermediate loop, the arrangement of the reactor vessel, and in-core changes will affect the efficiency of the SFR. These include the option of diluent grading in the fuel, flattening of the core outlet temperature profile, choosing Rankine or S-CO 2 for the balance of plant, and heat exchanger design. All these have been evaluated for their impact on plant efficiency. It has been determined that the S-CO 2 recompression cycle can provide efficiency benefits over conventional Rankine cycles for SFRs with core outlet temperatures at or above 510 o C. With the S-CO 2 cycle, SFRs can achieve thermal efficiencies of ~42 %. Thesis Co-supervisor: Prof. Michael J. Driscoll Title: Professor Emeritus of Nuclear Science and Engineering Thesis Co-supervisor: Prof. Neil E. Todreas Title: Professor Emeritus of Nuclear Science and Engineering Thesis Co-supervisor: Dr. Pavel Hejzlar Title: Principal Research Scientist 4

5 Acknowledgments First, I would like to thank Dr. Pavel Hejzlar for his patience, encouragement, and continual assistance in completing my thesis. His guidance was crucial to every part of my research, from the very beginning. Professors Michael J. Driscoll and Neil E. Todreas were ever-present, and their vast knowledge and experience kept me from falling victim to innumerable blunders. Jonathan P. Gibbs assisted me with my initial familiarization with the S- CO 2 cycle and CYCLES II and Anna Nikiforova helped to introduce me to heat exchanger modeling. Matthew Denman and Matthew Memmott have been great sources of background information on SFRs, having devoted many months to the DOE/NERI project on SFRs. Tri Trinh provided constant feedback on the compressor models and insight into the transient behavior of the recompression cycle. Thermoflow, Inc. has my appreciation for furnishing a free academic license for their software to the Department of Nuclear Science and Engineering. The steam cycle calculations were much simplified with this tool. My thesis spans several aspects of the work done in the Nuclear Science and Engineering Department and at MIT at large for that matter. Compressors, heat exchangers, and SFRs have brought me in touch with many students and faculty at MIT to whom I am grateful for their expertise and assistance. I have received support for this research from a NERI/DOE investigation of SFRs and a Sandia National Laboratories project on the S-CO 2 power cycle. 5

6 Table of Contents ABSTRACT..3 ACKNOWLEDGEMENTS....5 TABLE OF CONTENTS.6 LIST OF FIGURES...10 LIST OF TABLES.12 ACRONYMS INTRODUCTION Motivation Sodium-Cooled Fast Reactor Background S-CO2 Recompression Cycle Background HEATRICTM Printed Circuit Heat Exchanger Background Thesis Outline 20 2 RECOMPRESSION CYCLE DEVELOPMENT Introduction CYCLES to CYCLES III Extended Use of the Legault Nomenclature Optimization and Single Point Calculations The Simple Recuperative Brayton Cycle Inclusion of other NIST Fluids Interfacing with TSCYCO The Ethane Cycle Fluid Impurities in the S-CO 2 Recompression Cycle Helium Additions for Leak Detection Air Impurities Chapter Summary Nomenclature for Chapter S-CO 2 COMPRESSOR DESIGN Introduction Developing Compressors for the S-CO2 Cycle The Need for a Compressor Model Compressor Background Real Gas Radial Compressor (RGRC) Code Issues with Earlier Codes CCDS/CCODS and Motivation for RGRC Development Basic Outline of the RGRC Code Variable Nomenclature Impeller Calculations Loss Calculations Vaneless Space and Diffuser Calculations 67 6

7 3.3.7 Off-Design Compressor Performance The Multi-Stage Code RGRCMS S-CO 2 Compressor Designs The Main Compressor Design The Recompressing Compressor Design Benchmarking RGRC and RGRCMS Chapter Summary Nomenclature for Chapter BALANCE OF PLANT OPTIONS Introduction Necessary Tools for Analysis Heat Losses in Intermediate Piping and Pumping Power of an SFR Alternate Fluids in the Intermediate Loop Eliminating the Intermediate Loop PCHE versus Shell-and-Tube Heat Exchangers The Shell-and-Tube Code SoSaT Expanding the Capabilities of the PCHE Codes Benchmarking Heat Exchanger Codes S-CO2, Traditional Rankine, or Supercritical Steam PCS Chapter Summary Nomenclature for Chapter INCREASING THE EFFICIENCY OF THE SFR Introduction Options for Increasing Core Outlet Temperature A Reference Design: The ABR Option Space Methodology Results of Efficiency Comparisons The Choice of Cycle Pressure for Rankine Cycles Chapter Summary SUMMARY, CONCLUSIONS AND RECCOMENDATIONS Summary Conclusions Conclusions on the S-CO 2 Cycle and its Compressors Conclusions on Sodium Fast Reactors Recommended Future Work S-CO 2 Compressors The S-CO 2 Cycle as a Whole SFR Heat Exchangers Safety and Availability Consequences of SFR Design Options Where to Obtain Codes used in this thesis..126 REFERENCES.127 7

8 APPENDIX A CYCLES III CODE MANUAL A.1 Introduction.132 A.2 Inputs and Outputs..132 A.3 Troubleshooting..134 A.4 Conclusion APPENDIX B RGRC AND RGRCMS CODE MANUAL.136 B.1 Introduction.136 B.2 Inputs and Outputs B.3 Recommendations and Trouble-Shooting B.4 Fluid Properties B.5 Conclusion APPENDIX C PCHE CODES MANUAL 143 C1. Introduction.143 C.2 Inputs and Outputs..143 C.3 Cautions with the PCHE codes C.4 Improvements to the PCHE Codes..145 C.5 Cost Estimates for PCHEs C.6 Conclusion APPENDIX D SoSaT CODE MANUAL..148 D.1 Introduction.148 D.2 Inputs and Outputs..148 D.3 Cautions and Considerations for SoSaT.151 D.4 Correlations and Supporting Information D.5 Conclusion

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10 List of Figures Figure 1.1: Arrangement of the primary IHX in a pool-type SFR Figure 1.2: The density spike near the critical point of CO 2 Figure 1.3: Heatric TM Printed Circuit Heat Exchangers Figure 1.4: PCHE with two S-CO 2 plates to each Na plate and a helium fill-gas plate Figure 2.1: The Simple Recuperative Brayton Cycle Figure 2.2: The S-CO 2 Recompression Cycle Figure 2.3: Turbine size comparison for different fluids Figure 2.4: Efficiency Comparison of S-CO 2 Recompression Cycle to other cycles Figure 2.5: Pipe paths in the Recompression Cycle of CYCLES III Figure 2.6: The original output res.txt from the original CYCLES Figure 2.7: The effect of impurities on the critical temperature of CO 2 Figure 2.8: The efficiency of a pure ethane simple cycle Figure 2.9: The effect of dissociation on the ethane cycle Figure 2.10: The effect of turbine inlet temperature on cycle efficiency Figure 2.11: The effect of a helium leak detection gas on the S-CO 2 cycle efficiency Figure 2.12: The compressor work as the helium mole fraction is changed Figure 2.13: The effect of air impurity on the S-CO 2 cycle Figure 3.1: Design ranges for different compressor types Figure 3.2: The meridional plane view of a typical centrifugal compressor Figure 3.3: A straight vaned diffuser Figure 3.4: Example compressor performance map showing the surge line Figure 3.5: Fast-running fluid property subroutines for S-CO 2 produced by Gong Figure 3.6: Range of Applicability for Gong s S-CO 2 property subroutines Figure 3.7: A single-stage main compressor map from CCODS showing unusual features Figure 3.8: The velocity triangles at impeller inlet and outlet Figure 3.9: A simplified schematic of an impeller showing the definition of backsweep angle Figure 3.10: The process for determining impeller performance Figure 3.11: The flow path in the vaneless space Figure 3.12: The pressure ratio of the main compressor for varying speeds Figure 3.13: The total-to-static efficiency of the main compressor for varying speeds Figure 3.14: The pressure ratio of the recompressing compressor for varying speeds Figure 3.15: The total-to-static efficiency of the two-stage recompressing compressor for varying speeds Figure 3.16: The pressure ratio of the modeled test compressor for varying speeds Figure 3.17: The total-to-static efficiency of the modeled test compressor for varying speeds Figure 4.1: Schematic of the intermediate loop Figure 4.2: The temperature drop in a 24 m long intermediate pipe Figure 4.3: Heat Lost in a 24 m long intermediate pipe Figure 4.4: The division of the tube length according to heat transfer regime in SoSaT Figure 4.6: Rankine Cycle efficiency as a function of temperature and pressure 10

11 Figure 5.1: The arrangement of components in the SFR balance of plant Figure 5.2: The design choices affecting efficiency that are considered in this study Figure 5.3: STEAM PRO 16 diagram of the Rankine Cycle Figure 5.4: Efficiency comparison with PCHEs for both the P-IHX and S-IHX Figure 5.5: Efficiency comparison with a PCHE for the P-IHX and a shell-and-tube S-IHX. Figure 5.6: Efficiency comparison with a shell-and-tube P-IHX and a PCHE for the S-IHX. Figure 5.7: Efficiency comparison with shell-and-tube heat exchangers for both the P-IHX and S-IHX. Figure 5.8: Efficiency comparison with no intermediate loop and a PCHE IHX Figure 5.9: Efficiency comparison with no intermediate loop and a shell-and-tube IHX Figure 5.10: Cost of JSFR steam generator for varying steam pressures Figure B.1: The RGRC input file Figure B.2: The beginning of an RGRC output file Figure C.1: The input file ihxna_hyb.in with representative values Figure C.2: The output file ihxna_hyb.out with representative values Figure D.1: The SoSaT input file, matching the steam generator of the JSFR Figure D.2: The SoSaT output file Figure D.3: The placement of the central downcomer in SoSaT 11

12 List of Tables Table 2.1: Critical points of fluids important to the Ethane Simple Cycle Table 2.2: Properties of selected fluids at their critical points Table 3.1: The operating points of the compressors in the recompression cycle Table 3.2: The non-dimensional parameters of the compressors in the recompression cycle Table 3.3: Selected Sandia Test Compressor Parameters Table 4.1: Representative Values used in Eqn. 4-1 Table 4.2: Intermediate Loop Pumping Power Requirements for SFRs Table 4.3: Characteristics of CRBR and ABR-1000 Intermediate Loops Table 4.4: Correction factors for the cross-flow Nusselt number Table 4.5: Conditions for each boiling regime in SoSaT Table 4.6: Benchmarking of the SoSaT Code Table 5.1: The reference balance of plant Table 5.2: Core Outlet Temperatures of Selected SFRs Table 5.3: Standard channel dimensions used for PCHEs in this study Table 5.4: Options Considered in the Efficiency study Table 5.5: Efficiency Comparison of SFR options for a core outlet temperature of 510 o C Table 5.6: Efficiency Comparison of SFR options for a core outlet temperature of 530 o C Table B.1: RGRC inputs and their suggested ranges Table C.1: Files needed for each PCHE code 12

13 Acronyms P-IHX S-IHX IHX PCHE S-CO 2 SFR PCS HTR LTR NIST ANL INL GTL RMS DNB CHF ASME ONB NACA IAEA NRC BOP BOL EOL MC RC TNF Primary Intermediate Heat Exchanger Secondary Intermediate Heat Exchanger Intermediate Heat Exchanger Printed Circuit Heat Exchanger Supercritical Carbon Dioxide Sodium-Cooled Fast Reactor Power Conversion System High Temperature Recuperator Low Temperature Recuperator National Institute of Standards and Technology Argonne National Laboratory Idaho National Laboratory Gas Turbine Laboratory (MIT) Root-Mean-Square Departure from Nucleate Boiling Regime Critical Heat Flux American Society of Mechanical Engineers Onset of Nucleate Boiling National Advisory Committee for Aeronautics International Atomic Energy Agency Nuclear Regulatory Commission Balance of Plant Beginning of Life End of Life Main Compressor Recompressing Compressor Technology Neutral Framework 13

14 1 Introduction 1.1 Motivation There are four primary objectives in this research. The first objective is to update the CYCLES II code with the abilities to model a system running on any fluid available in the NIST database and to model either simple or recompression cycles. The code should also be as userfriendly as possible owing to the fact that it may be used by many students who will have to become familiar with it in a short period of time. Its applicability as a research tool will be enhanced to include any simple Brayton cycle and more flexible investigations of the recompression cycle. The second objective is to develop models for single and multi-stage centrifugal CO 2 compressors using a user-friendly computer code which will be developed as part of this research. The code will fill in gaps in MIT s capability to model turbomachinery performance and will enable transient models of the recompression cycle to more accurately incorporate compressor performance. The third objective is to perform a preliminary investigation of the intermediate loop and heat exchangers (IHX) that might be used in an SFR. This investigation will focus on cost, size, and efficiency. Fourth, the investigation will look into the range of options for increasing the efficiency of the SFR. All of these objectives will enhance the work being done on Sodium-Cooled Fast Reactors and the S-CO 2 Power Conversion Systems that might be used as a balance of plant in a number of next-generation power reactors including the SFR. This study will compare heat exchangers, and power cycles based on an assumed thermal power of 250 MW, modeled after the thermal power of a single loop in the ABR S-CO 2 recompression cycles and their associated compressors are modeled on an assumed cycle thermal power of 500 MW. This value was selected because compressors become difficult to design for an operating speed of 3600 RPM in smaller power systems and two heat exchanger loops could be coupled to a single turbomachinery train. The operating speed of 3600 RPM is selected in order to synchronize the cycle to the electric grid. These restrictions on compressor design are discussed further in Chapter Sodium-Cooled Fast Reactor Background Sodium-Cooled Fast Reactors have been operated in the United States since EBR-1 in 1951 [IAEA, 2006]. They are currently of interest as a means to manage actinides from LWR spent fuel. The SFR is assumed to be one of two types: a pool design in which the primary sodium flows from a lower cold pool up through the core and into an upper hot pool, or a loop design in which the primary sodium exits the reactor vessel and flows through a heat exchanger, 14

15 returning in a cold leg to the core inlet. The primary intermediate heat exchanger, which transfers heat from radioactive primary sodium to clean intermediate sodium, is located within the reactor vessel in a pool design, and outside the vessel in the loop design. The pool design essentially eliminates the loss of coolant accident (LOCA) sequence, while the loop design reduces the amount of primary coolant and saves capital cost by reducing the size of the vessel. Figure 1.1 schematically shows the pool-type design option. The P-IHX is located within the vessel, whereas a loop-type design would require pumping primary sodium through primary piping to a P-IHX outside the vessel. Both designs employ an intermediate sodium loop which serves as a buffer between the radioactive primary coolant and the power conversion system (PCS). Figure 1.1: Arrangement of the primary IHX in a pool-type SFR. Primary sodium flows downward through the P-IHX and into the cold pool. Primary pumps located within the cold pool pump the sodium back up through the core. In this way the hot and cold pools are separated by what is called a redan. With the intermediate loop present, steam generator leaks will not release any activated sodium and will constitute less of a safety risk. SFRs operate with core outlet temperatures up to 575 o C, as in the BN-1800 design [IAEA, 2006]. They typically have a temperature rise across the core of less than 200 o C which makes them well suited for the S-CO 2 recompression cycle because it is so highly recuperative. Fuels can be metal or oxide and SFR cores can be designed with conversion ratios from 0 to 1, or above. The advantages of SFRs are the excellent heat transfer characteristics of sodium, excellent material performance in a sodium environment, and high temperatures. Large-scale SFRs have been operated around the world with varying success. 15

16 1.3 S-CO 2 Recompression Cycle Background Increasing cycle efficiency and reducing capital costs are the best ways to reduce electricity costs in the nuclear power industry. There is great interest in new balance of plant options that maximize efficiency while reducing plant capital costs. Closed Brayton cycles are simple and compact and can achieve very high efficiencies at the proper conditions. The most interesting of these is the supercritical CO 2 recompression cycle. Much of this thesis is devoted to the S-CO 2 recompression cycle because it is so promising for applications with core outlet temperatures above 500 o C. Other Brayton cycles, like the helium Brayton cycle, achieve very high efficiencies at much higher temperatures. These high temperatures, however, are much more challenging to materials than the S-CO 2 recompression cycle. S-CO 2 recompression cycles have been investigated at MIT for several years, beginning in 2000 [Dostal, 2004]. The use of CO 2 as a working fluid in power conversion systems has enjoyed success in British gas-cooled reactors (GCR) and has been studied by since the 1960 s [Dostal, 2004], but the operating range of industry experience has not produced much data in the supercritical regime. The recompression cycle has significant advantages over other cycles, and especially over other Brayton cycles for turbine inlet temperatures above 490 o C. The ability of the S-CO 2 cycle to reach high efficiency comes from the reduced compressor work as the compressor inlet conditions approach the critical point of CO 2. The density of the fluid increases dramatically, as shown in Figure 1.2. The increased density close to the critical point reduces the compressor work. 16

17 Figure 1.2: The density spike near the critical point of CO 2. As the temperature decreases and approaches the critical temperature (indicated with the red line), the density rises more rapidly [NIST, 2007]. Earlier research on the S-CO 2 cycle by Vaclav Dostal sized components and calculated efficiencies of the S-CO 2 recompression cycle. Dostal s research optimized heat exchanger sizes, roughly sized turbomachinery, and showed that the S-CO 2 cycle could be economically competitive, especially at higher turbine inlet temperatures [Dostal, 2004] through the use of a steady state code called CYCLES. This work has been continued and studies of the steady-state and transient cycle performance have been conducted through the use of computer codes at MIT and in an experimental compression loop operated by Sandia National Laboratory in collaboration with Barber-Nichols Inc. [Wright et al., 2008]. CYCLES III is the result of updates to Dostal s CYCLES and its operation is detailed in Chapter 2. It is a steady-state code that models the recompression cycle as well as the simplerecuperative Brayton cycle. It models compressors simply, because it is operating at steady state and the user inputs a value for the compressor efficiency. More information is needed about how compressors will operate in the recompression cycle, so the development of a mean-line compressor design and performance code (RGRC) was undertaken in this research. RGRC is detailed in Chapter 3 and has produced compressor performance maps which are useful to 17

18 transient analyses as well as to steady-state studies which require a value for compressor efficiency. The recompression cycle is interesting to next generation nuclear reactors because it achieves high efficiencies, especially at high turbine inlet temperatures. The turbomachinery is compact and sodium reactions with CO 2 are less exothermic than sodium reactions with water. The working fluid, CO 2, is abundant, non-toxic, and cheap. It appears that at higher temperatures (500 o C and up), the S-CO 2 cycle can outperform the Rankine cycle, but even if the advantage is moderate, the compactness of the S-CO 2 cycle may be a very significant savings in cost and space. This compactness has made the cycle a consideration for such applications as space and naval power cycles. 1.4 HEATRIC TM Printed Circuit Heat Exchanger Background HEATRIC TM Printed Circuit Heat Exchangers (PCHEs) are discussed often in this research. They are the heat exchanger of choice for compactness and ruggedness. They are formed by diffusion bonding plates with etched channels. Alternating plates for hot and cold fluids allow for very high heat transfer area in a relatively compact volume. Figure 1.3 shows the stacking of hot and cold PCHE plates and the cross section of semi-circular etched channels. PCHEs have been modeled at MIT with Fortran codes written by Pavel Hejzlar [Hejzlar et al., 2007] and updated by several others [Shirvan, 2009]. Figure 1.3: Heatric TM Printed Circuit Heat Exchangers are formed by diffusion bonding stacked plates (left) of alternating hot and cold fluid channels. This creates a monolithic block of parallel channels (right). [Heatric, 2009] PCHEs can be built with a varied range of channel diameters, but they are, in general, very small. The PCHEs used in this models discussed here have channel diameters of 2.5 mm. They can be constructed with alternating hot and cold plates, one hot plate for two cold plates, etc. They have the option of producing hybrid designs which include a separating plate with fill gas channels for leak detection, as shown in Figure

19 Unit cell S-CO 2 plate S-CO 2 plate Helium plate Sodium plate Helium plate S-CO 2 plate S-CO 2 plate Figure 1.4: PCHE with two S-CO 2 plates to each Na plate and a helium fill-gas plate in between [Ludington et al., 2007]. The channels can be either straight or zig-zag channels, but are usually straight for sodium. Zigzag channels improve the heat transfer coefficient by a factor of ~2.3, but have a pressure drop penalty. The PCHE codes at MIT model the heat transfer by nodalizing the heat exchanger core along the flow path and iterating along the heat exchanger length. A heat balance is solved for each node until the desired power is reached. Simplifying assumptions used in the PCHE models are very similar to those made in modeling shell-and-tube heat exchangers in Chapter 4. For the PCHE, they are: 1. Mass flow of each fluid is uniformly distributed among the channels. 2. Every unit cell has the same temperature within the heat exchanger core. 3. The wall channel is uniform around the channel periphery. 4. Zero heat is lost and axial conduction is negligible. 5. Kinetic and potential energy are neglected 6. Fluid properties are constant along a node. The total heat transfer coefficient is determined using correlations appropriate to the fluids being used and, in the case of PCHEs with a helium plate, by adjusting the conduction length of the plates to account for the thermal resistance of the helium channels. Detailed discussion of the solution methodology is available from Dostal [2004]. PCHEs, in general, have high power density. Leaks can be controlled by using the helium hybrid plate, but the small channels also mean that a single leak will not be likely to pose serious problems. Pumping sodium through narrow channels has been avoided in the past, but recent research shows that clean sodium can be pumped through narrow channels without 19

20 problems [Hejzlar, 2008]. These benefits make PCHEs very appealing for applications where compact heat exchangers are desirable. 1.5 Thesis Outline Chapter 2: Recompression Cycle Optimization Chapter 2 details the changes made to the CYCLES II code for modeling the Recompression cycle, in addition to the history of the code and its capabilities. Also in this chapter are discussions of fluid impurities and detection gases, heat exchanger sizing, and the affects all these have on cycle efficiency. A discussion of the recompression cycle as compared to other cycles is also included. In addition, a brief study of an Ethane simple recuperative Brayton cycle is discussed. Chapter 3: S-CO 2 Compressor Design This chapter details the history of S-CO 2 compressors and the code, RGRC, developed in this work as a mean-line design code for real gases. For the reader unfamiliar with compressor design and operation, an overview of these topics is included as well. Detailed discussion of the code s operation and results are presented. The compressors are developed to run with a 500 MWth recompression cycle to scale with the 250 MWth heat exchangers considered in Chapters 4 and 5. The compressor designs are chosen to produce both efficient and versatile compressors. An attempt at benchmarking has been made by using estimated geometry for an existing test compressor [Wright et al., 2008]. Chapter 4: Balance of Plant Options for the SFR Chapter 4 discusses the ex-core options for the SFR, from an efficiency focused perspective. Tools developed for modeling the S-CO 2 recompression cycle are used to compare its performance to that of supercritical steam and conventional Rankine plants. Different configurations of the plant, including elimination of the intermediate loop, are considered. Computer codes for modeling heat exchangers are discussed, as well as the impact of the intermediate loop on efficiency. Chapter 5: Increasing SFR Efficiencies Chapter 5 details the changes that can be made within the core and choices in the balance of plant that improve the efficiency of the SFR. Any such effort is primarily aimed at improving the turbine inlet temperature. At higher temperatures differences between power cycles become important. Comparisons are made between several different configuration options and discussions of safety and cost are included with the efficiency results. The design configurations 20

21 considered span every combination of PCHEs and shell-and-tube heat exchangers within sizing constraints. Unless otherwise noted, all fluid properties have been computed using REFPROP 8.0, available from the National Institutes of Standards and Technology (NIST) [NIST, 2007]. For compressor development fluid properties in Chapter 3 have been calculated using faster polynomial subroutines for CO 2. These are discussed in Chapter 3. Sodium properties come from experimental temperature-dependent relationships developed at Argonne National Laboratory [Fink and Leibowitz, 1995]. 21

22 2 Recompression Cycle Development 2.1 Introduction The S-CO 2 recompression cycle is a variation of the well-known simple recuperative Brayton cycle. The open Brayton cycle is familiar to anyone who has flown on a commercial jetliner. Closed Brayton cycles are used in power conversion systems (PCS) with a variety of working fluids. The simple closed cycle is used with helium, CO 2, or gas mixtures in a variety of engineering applications. Figure 2.1 shows the simple recuperative Brayton cycle schematic and its T-s diagram for ideal components. Figure 2.1: The Simple Recuperative Brayton Cycle The simple recuperative Brayton cycle includes a heat exchanger (recuperator) as shown in Figure 2-1. This recuperator preheats the fluid entering the reactor (IHX) with energy from 22

23 the turbine exhaust. The precooler is the mechanism for heat rejection to the environment from the S-CO 2 cycle. The precooler outlet (state 1) is just above the critical point of the fluid, reducing the work of the compressor and thus enhancing efficiency. With CO 2 as the working fluid, the simple recuperative cycle does not achieve attractive efficiencies because heat transfer is not effective in the recuperator. The reason is the development of a pinch-point in the recuperator. Pinch -point refers to the location along the heat exchanger width at which the temperature difference between the hot stream and the cold stream reaches zero. At that point no more heat transfer will occur, resulting in very poor recuperator effectiveness. The underlying cause of the pinch-point in a simple recuperative cycle is the mismatch in specific heats at different pressures of the two streams. The solution to this problem is the recompression cycle, shown in Figure 2.2. By splitting the recuperator into a low temperature recuperator (LTR) and a high temperature recuperator (HTR), the pinch-point problem is avoided. The flow is split and two compressors are needed [Dostal, 2004]. Figure 2.2: The S-CO 2 Recompression Cycle 23

24 The recompression cycle is designed with two recuperators and two compressors because of the pinch-point problem that arises if a simple recuperative cycle is used [Dostal, 2004]. Flow is split at the inlet to the precooler (point 6 in Figure 2.2) and then merges again at the inlet to the cold side of the HTR (point 2 in Figure 2.2). Typically about 38% to 40 % of the flow will be directed to the recompressing compressor. Without using the recompression cycle, large differences in specific heat capacity cause the temperature difference in the recuperator of the simple Brayton cycle to reach zero; a pinch-point. The result of the pinch-point problem is poor effectiveness in the recuperator and lower cycle efficiency. The recompression cycle can achieve thermal efficiencies far superior to those of any existing LWR if the turbine inlet temperature is sufficiently high. S-CO 2 cycles become competitive at turbine inlet temperatures of about 490 o C. This temperature threshold makes the S-CO 2 recompression cycle attractive to next-generation plants, like SFRs, because core outlet temperatures will likely be in the range of 500 o C to 550 o C. Besides efficiency, another benefit of the S-CO 2 cycle is its compactness. The turbine, for example, is an order of magnitude smaller in an S-CO 2 plant than in most other power cycles. Figure 2.3 shows the size comparison of the CO 2 turbine with those of helium and steam cycles as developed by Dostal [2004]. Figure 2.3: Turbine size comparison for different fluids, from Dostal, [2004] Small turbomachinery and relatively small heat exchangers mean that capital costs and plant footprint can be reduced. The ability to model this cycle and predict efficiency is critical to evaluating its competitiveness with other cycles. 24

25 The compressors and the turbine are assumed to run on a single shaft in the recompression cycle in order to simplify the design and reduce capital costs. This method introduces controllability issues, however, and the transient operation of the cycle must use finely tuned controllers. The main compressor inlet runs very near the critical point of CO 2, where fluid properties are highly variable. Therefore, the performance of the cycle is very sensitive to control of the main compressor inlet conditions. Aspects of cycle control are discussed in Tri Trinh s SM thesis and he has developed a code (TSCYCO) that models the cycle under a variety of transients [Trinh, 2009], [Kao, 1984]. TSCYCO models the response of the entire PCS and allows the user to adjust parameters which operate a set of control valves. Dostal s main goal in CYCLES was to size heat exchangers and to optimize the configuration of the recompression cycle for maximum efficiency. Optimizing the S-CO 2 cycle allows for a comparison with the traditional Rankine cycle, to determine whether the cycle can achieve economic competitiveness beyond that of Gen III+ reactors when coupled to Gen IV reactor designs like the SFR. Dostal s results showed that the S-CO 2 cycle can be very competitive in efficiency, especially as turbine inlet conditions are increased, as shown in Figure 2.4. Figure 2.4: Efficiency Comparison of S-CO 2 Recompression Cycle and other Cycles [Dostal, 2004] 2.2 CYCLES to CYCLES III CYCLES III is the latest edition of a code that models the performance of an S-CO 2 power conversion system, for either a simple recuperative Brayton cycle or a Recompression cycle. It was originally written as CYCLES by Vaclav Dostal and was used as the main analysis 25

26 tool in his Ph.D. work [Dostal, 2004]. The original CYCLES included no piping losses and only performed calculations for the recompression cycle. Subsequent improvements by Pavel Hejzlar and David Legault [Legault, 2006] improved the code to include pipe modeling, and a much more readable, user-friendly structure and variable nomenclature. Legault s improvements made the code much more accessible to new users because the variable names are very logically constructed. Legault named his code CYCLES II, but the code still only performed recompression cycle calculations. The simple, recuperative Brayton cycle is typically used in the nuclear power industry with helium as the working fluid, and can reach efficiencies superior to LWRs. High Temperature Gas-cooled Reactors (HTGRs) can reach efficiencies of % and the Modular Pebble Bed Reactor (MPBR) is expected to reach efficiencies approaching 45 % [Wang, 2003]. The ability to model the simple cycle is included in CYCLES III, as a comparison with the recompression cycle and so that the code is useful for more applications. The main improvements in CYCLES II were the inclusion of a detailed pipe model and the consolidation of the input and output files. Figure 2.5 shows the numbering scheme applied to the pipe paths in CYCLES III for the recompression cycle > <--PRE >----7 \/ \/ ^ MCOMP=========RECOMP===========TURBINE 12 ^ \/ ^ \/ > >---4 ^ 2-->-LTR<--< <--HTR->-5>-IHX ^ < <----9 Figure 2.5: Pipe paths in the Recompression Cycle of CYCLES III Each of the twelve paths shown in Figure 2.5 has detailed information about the dimensions of the pipes, to allow for the effect of pressure drop on efficiency. Legault was able to show, with Hejzlar s detailed pipe model, that the pressure drops within pipes and plena were important to the efficiency of the cycle [Legault, 2006]. Piping losses can reduce the efficiency of the plant by as much as 2.0 %, depending on the design of the piping. Consolidating the 26

27 input and output files made the code much easier to use. For the user, these input and output files made the information very readable, and the files could be used in papers and presentations without significantly altering their format. CYCLES II eliminated Dostal s option of optimizing heat exchanger volumes. CYCLES II, therefore could only produce results for the cycle defined by the user and the user would have to make judgments about how to size the heat exchangers. The goal with CYCLES III was to include all of the best features of the previous editions, along with some new features. After completion, the new developments in CYCLES III are: 1. Extended use of the easy to read Legault code structure and nomenclature 2. Inclusion of both optimization and single point calculations 3. Inclusion of both Simple and Recompression Cycles 4. The ability to model impure working fluids (or a variety of different working fluids) 5. An interface for the headers in TSCYCO 6. A convenient code manual (see Appendix A) for troubleshooting Extended Use of the Legault Nomenclature CYCLES II incorporated an easy to read nomenclature, but Legault recommended that the use of it be extended further into some of the subroutines and that the structure should be simplified further. Though it may be contrary to some programmers preference, the use of a large variable module has been incorporated in CYCLES III so that the program code is easily readable and understandable for new users. Variable names are more intuitive than in the original CYCLES. For example, Legault changed temperature variables in the LTR from Dostal s structure: trl(1) inlet temperature of the cold side ( C) trl(2) outlet temperature of the cold side ( C) trl(3) (not used) trl(4) inlet temperature of the hot side ( C) trl(5) real outlet temperature of the hot side ( C) trl(6) ideal outlet temperature of the hot side ( C) to a derived type structure that looks like: ltr.tincold inlet temperature of the cold side (K) ltr.toutcold outlet temperature of the cold side (K) ltr.tinhot inlet temperature of the hot side (K) ltr.touthot real outlet temperature of the hot side (K) ltr.touthoti ideal outlet temperature of the hot side (K) 27

28 Legault used similar derived-type structures for enthalpy, pressure, entropy, density, and many other characteristics of the LTR. Likewise, the HTR, pre-cooler, turbine, and compressors have their own variable names with derived-type structures. These are contained in the file modglobalvariables.f90. This file has undergone only minor changes from CYCLES II to III. A new data type, optdata has been added. It consists of dimensions for the heat exchangers so the code can read through optimization results and select the dimensions consistent with the highest efficiency while optimizing the cycle. Other small changes include the addition of a throttle on the compressors. An input has been added so that the user can define a form loss coefficient to represent the throttle. These inputs are explained more in Appendix A. The form loss is necessary because, as TSCYCO shows, compressor throttles must be in the partially closed position at steady state operation in order to allow for controllability during transients. Form loss coefficients can be based upon experience from operating TSCYCO. In CYCLES III, Legault s nomenclature was expanded to the subroutines that compute the performance of each component of the cycle. The variable module modglobalvariables has been expanded to: EXPAND COMPRESS PCHEVOL PRECOOLER The subroutine for the turbine The subroutine for compressors The recuperator subroutine The precooler subroutine This increases the general readability of the code Optimization and Single Point Calculations The optimization function available in Dostal s original CYCLES has been returned in CYCLES III. The code is easier to use than the original because it simplifies the outputs for the user and minimizes the manipulation of data required on the part of the user. The optimization approach is brute force, iterating from an initial guess of recuperator volumes until the efficiencies of many different configurations have been examined. The heat exchangers in the S- CO 2 cycle are assumed to be counter-flow PCHEs, without a detection gas plate. Optimization is performed by selecting a total volume of heat exchangers. This total volume will then be divided among the pre-cooler, High Temperature Recuperator (HTR), and Low Temperature Recuperator (LTR) until the configuration of highest efficiency is found. In the original CYCLES, an output file called res.txt listed heat exchanger volumes and the resultant cycle efficiency, as shown in Figure

29 Figure 2.6: The original output res.txt from the original CYCLES. The code user then had to pick through the output to find the configuration which yielded the highest efficiency. The optimization output included forty parameters of the cycle, far more than necessary to perform an optimization. Heat exchanger volumes are not even visible when the file is opened, because they are so far to the right in the text. In subroutines named OPTIMIZE_R and OPTIMIZE_S, for the recompression and simple cycles respectively, CYCLES III performs this calculation and then steps through all of the results in res.txt to locate the optimum configuration without burdening the user with the task. As the code steps through the optimization results, the heat exchanger dimensions are stored in optdata, replacing the dimensions each time a configuration of higher efficiency is found. Once res.txt has been read, the code calculates the performance of the cycle having heat exchanger dimensions defined by optdata and then outputs the results The Simple Recuperative Brayton Cycle Including the Simple Recuperative Brayton cycle in CYCLES III allows the user to quantify the efficiency gain that is achieved by using the Recompression cycle. It also makes CYCLES III a useful tool for designers in power conversion systems using other NIST fluids, a new capability discussed in Section Coding of the cycle calculations for the simple cycle in CYCLES III was based on the structure of the code for the recompression cycle in CYCLES II. If the user looks into the code, he or she will find that the file simple.f90 looks almost identical to the file recompress.f90. It has been modeled after Legault s structure so that the user 29

30 can easily transfer knowledge and experience between the two. Choosing the simple cycle or the recompression cycle is as easy as changing the value of itype in the input file HXdata.txt. The simple cycle can be used to model typical helium Brayton cycles. Investigation will show that a simple cycle will run with S-CO 2, but cycle efficiencies will be too low to ever be viable in industrial use Inclusion of other NIST Fluids The most drastic change in CYCLES III, in terms of functionality, is the ability to model the cycle with any NIST fluid and mixtures of NIST fluids. CYCLES III determines fluid properties from highly developed polynomials, available from the National Institute of Standards and Technology (NIST). These polynomials are available through Fortran subroutines, but can be slow to use if many calculations are needed [NIST, 2007]. To speed up calculations, CYCLES has always included the ability to develop tabulated fluid properties from these polynomials. Once the tables are complete, the code can run much faster, however, the original table creation subroutines were written only for pure fluids. It is certain that no working fluid can be entirely pure, and that impurities will change the critical point of the mixture. Figure 2.7 shows the effect of a few impurities on the critical point of CO 2. The critical point can be identified by the spike in heat capacity at constant pressure. 30

31 Figure 2.7: The effect of impurities on the critical temperature of CO 2. The molar specific heat capacities of CO 2 mixtures are shown for lines of constant pressure. a.) pure, b.) 1% H 2 by mole fraction, c.) 1% Propane by mole fraction The modifications in CYCLES III allow the user to include any fluid available in the NIST database as an impurity, including an approximation for air. The input file HXdata.txt includes a portion near the top that reads: 31

32 0!ifluid This is the first fluid, 0-CO2, 1-Ethane, 2-Helium 1!mix IDs if there is a 2nd fluid, 0-pure, 1-2nd fluid exists 2!ifltwo IDs 2nd fluid, 0-He, 1-Air,2-Hydrogen,3-Nitrogen,4-Methane 0.010d0!fracgas This is the mole fraction of the 2nd fluid(if applicable) The inputs listed above would correspond to the mixture shown in Figure 2.6b. Air is included in CYCLES III as a mixture of % N 2, % O 2, and 0.92 % Ar by mole fraction, as approximated in NIST s REFPROP program. The computing time required to develop tables is much longer for mixtures, but it is necessary because the effect of impurities can be substantial, as discussed in Section 2.4. The user could choose to modify the code and change the available NIST fluids, simply by changing the reference fluid property file called by CYCLES III. This is discussed in Appendix A. The ability to model the cycle with other fluids is especially useful in the simple cycle, because the simple cycle has been used in many industries, with several different working fluids. Research into new power cycles can take advantage of this capability, as discussed further in Section Interfacing with TSCYCO The Transient S-CO 2 Cycles Code (TSCYCO) is Tri Trinh s updated version of Shih Ping Kao s S-CO 2 Power Systems (SCPS) code [Trinh, 2009], [Kao, 1984]. TSCYCO performs transient analysis of the S-CO 2 recompression cycle for several different transients based on energy, mass, and momentum conservation laws. Its function is very different from that of CYCLES III, but it does require information about the structure of the piping that is in a different format than CYCLES III. The headers in TSCYCO are modeled as single equivalent pipes, one for each of the twelve paths in Figure 2-5. The required dimensions are: The total internal volume of the header The thickness of the equivalent pipe The length and diameter of the header The total heat transfer area of the header Because each path in Figure 2.5 has a single header in TSCYCO, CYCLES III lumps all the passages in each of the twelve paths into one header, preserving total volume of steel, total internal volume, and pressure drop. Because transient effects depend on mass flow rates, and therefore accumulations of mass, the volumes of the headers are important. These are preserved from CYCLES III in a rough approximation based on the hydraulic diameter of each passage in 32

33 the detailed pipe model of CYCLES III. Because of the thermal inertia of the pipes steel, an approximation of the volume of steel is made for each header based on the ASME required thickness of an equivalent pipe. The ASME minimum required thickness for a circular pipe is given by PD t Eqn S + Py where t is the pipe s thickness, P is the internal pressure, S is the maximum allowable stress intensity for the material, y is a safety factor equal to 0.4, and D is the outside diameter of the pipe [ASME, 2007]. In CYCLES III, the subroutine HEADERS calculates the header dimensions for TSCYCO by determining approximate: Heat transfer areas, Volumes of steel, and Internal pipe volumes for each of the twelve paths. Then each path is recreated as a single pipe by increasing the length of the pipe and adjusting dimensions to preserve the three quantities listed above. The length is increased until the pressure drop of the header matches that calculated in CYCLES III for the path. Pressure drops are calculated as P = f 2 ρv2 L D + k 2 ρv2 Eqn. 2-2 where ρ is the fluid density, v is the velocity, L is the header length, D is the header diameter, k is a form loss coefficient, and the friction factor, f, is determined from the Blasius correlation for low Reynolds numbers and the McAdams correlation for higher Reynolds numbers [Todreas and Kazimi 1993]. f = 0.316Re 0.25, Blasius correlaion: Re < 30, Re 0.20, McAdams correlation: Re 30,000 Eqn. 2-3 For every pipe in CYCLES III, the form loss factor k was assumed to be This comes from a contribution of 1.0 for fluid expansion and 0.5 for fluid contraction at the pipe outlets and inlets, respectively. The dimensions and pressure drops are presented as output in headers.txt. CYCLES III and TSCYCO showed good agreement in the header calculations, producing pressure drops that matched by + 5 % at TSCYCO s steady state [Trinh, 2009]. 33

34 Another change to CYCLES III was the inclusion of form losses at each compressor outlet. These losses are due to the throttles required in a real design for controllability. In TSCYCO, the controllers can be tuned to provide adequate controllability, but throttles must be partially closed in steady state operation. The losses associated with partially closed throttles can be represented in CYCLES III by the form loss coefficients Kmc and Krc for the main and recompressing compressors respectively. 2.3 The Ethane Cycle The increased capabilities of CYCLES III allowed modeling of a simple recuperative ethane cycle, to determine if it could be cost competitive for electricity production. Hejzlar and Driscoll noted that the critical point of ethane makes it appealing for use in power cycles, due to the advantage of the low compressor work as in the S-CO 2 cycle [Driscoll and Hejzlar, 2007]. Ethane dissociates at high temperatures into myriad hydrocarbons. The dominant dissociation reactions are C 2 H 6 2CH 3 Eqn. 2-4 CH 3 + C 2 H 6 CH 4 + C 2 H 5 Eqn C 2 H 5 2C 2 H 4 + H 2 Eqn. 2-6 producing methane (CH 4 ), ethylene (C 2 H 4 ), and hydrogen as major constituents of the dissociated mixture [Perez, 2008]. Other reactions result in the presence of propylene (C 3 H 6 ), propane (C 3 H 8 ), and butane (C 4 H 10 ), though to lesser, but still not well known, degrees. The critical points of methane and ethylene are such that they hurt the efficiency of the ethane cycle. High pressures suppress the dissociation, so it is difficult to determine the extent to which dissociation will occur. Table 2-1 shows the critical points of pure ethane (C 2 H 6 ), methane (CH 4 ), ethylene (C 2 H 4 ), and the dissociated mixture. The mixture is expected to undergo very high dissociation at PCS temperatures. For example, the equilibrium concentration of ethane after temperature has been increased to ~700 K is only ~55 % at 20 MPa [Perez, 2008]. 34

35 Cycle Efficiency (%) Table 2.1: Critical points of fluids important to the Ethane Simple Cycle Critical Temp. (K) Critical Press. (MPa) Critical Dens. (kg/m 3 ) Ethane Methane Ethylene Hydrogen Modeling the simple Brayton cycle in CYCLES III, pure ethane can achieve high efficiencies as shown in Figure 2.8 for a range of turbine inlet temperatures Turbine Inlet Temperature ( o C) Figure 2.8: The efficiency of the pure ethane simple cycle The simplicity of the cycle, high efficiency, and the easy availability of ethane made this concept very appealing. In a real system, some of the ethane must dissociate, but if the critical point was not impacted too greatly high efficiencies might still be achievable. Ethane/methane mixtures were used in CYCLES III to model the behavior of the simple cycle under different dissociation conditions since the real dissociation effects are not well known. Ethylene was not included because the REFPROP data for ethylene only extends to a temperature of 450 K. The critical point of ethylene is not as damaging to the cycle as that of methane is, so the use of methane impurities only should still give a good assessment of how dissociation affects cycle efficiency. Hydrogen is not expected to appear in large portions, but the critical point of hydrogen is so low that its presence will be very detrimental to cycle efficiency. Figure

36 Cycle Efficiency (%) shows the effects of methane concentration on the ethane cycle operating with a turbine inlet temperature of 470 o C. This turbine inlet temperature was chosen because the applicable range of methane data in REFPROP is also limited by temperature Methane Content (mole %) Figure 2.9: The effect of dissociation on the ethane cycle After a methane concentration of 20 % by mole, the efficiency loss is approximately linear with methane percentage. Equilibrium concentrations of ethane at the high temperatures of the cycle are less than 60 %. At the expected level of dissociation, the simple ethane cycle fails to perform beyond the efficiencies achieved in current LWRs. As mentioned in Chapter 1, other simple gas cycles running on helium have achieved very high efficiencies. Unless experiments show that dissociation does not occur nearly to the predicted levels or that recombination mitigates reverses the process at low temperature, the ethane simple cycle cannot be viable for economic power conversion systems. Also, the flammability of ethane and methane introduces problems for safety. 2.4 Fluid Impurities in the S-CO 2 Recompression Cycle The performance of the recompression cycle is attractive because the main compressor operates just above the critical point, reducing compressor work a great deal. The critical point of CO 2 is at MPa and o C. The low dissociation and low corrosion rates of CO 2, and temperature of commonly available cooling water mean that CO 2 is a good choice for working fluid. Inevitably present impurities in the fluid will change the critical point. Compressor work will rise if the critical point is lowered from that of pure CO 2 as the compressor inlet conditions become further from the critical point. Cooling water puts a lower limit on the temperature of 36

37 the fluid at the inlet to the main compressor. In order to predict the effect of expected impurities or a detection gas on cycle performance, optimized cycles were run on a series of different fluids. A detection gas is desirable in many cases because the S-CO 2 cycle could be used as a direct cycle. In a direct cycle, detecting CO 2 leaks would warn of a primary system rupture before the problem became dire. For SFRs, sodium reacts exothermically with CO 2, so detecting leaks early can prevent major problems. Helium is frequently used as a detection gas because it reveals leaks sooner than almost any other gas (due to its small atomic size). Also, it usually has minimal detrimental effect on engineering systems because it is chemically inert. Other options for a detection gas could be any chemical lighter than CO 2 that doesn t significantly lower the critical temperature. Air is inevitably present as an impurity in any gas purchased for industrial use. The cost of gases depends strongly on their purity as well. Studying the amount of air tolerable in an S- CO 2 cycle will help to reduce the operating cost of the cycle by reducing the required purity of the working fluid. It will also let designers know what level of air impurity can be tolerated before they can expect the efficiency of the system to be unacceptably low Helium Additions for Leak Detection Based on a 2400 MWth, 4 loop design, it is estimated that 0.5 mole percent helium is needed to detect leaks in the CO 2 recompression cycle [Freas, 2007]. At 600 MWth per loop, this estimate can be applied to the recompression loop studied here. Recompression cycles will likely be built for 400 MWth or larger systems (per loop) because of the constraints on compressor design, as discussed in Chapter 3. Shifting the critical temperature to too low a value will cause the cycle to lose efficiency because cooling water temperature cannot be drastically changed. Shifting it to too high a value will cause the main compressor inlet state-point to fall below the vapor dome, a consequence to be avoided. Some test results, however, show that operation below the vapor dome is not necessarily damaging to the system [Hejzlar, 2008b]. The critical points of gases discussed in this chapter are shown in Table

38 Net Cycle Efficiency (%) Table 2.2: Properties of selected fluids at their critical points Added Constituent Critical Pressure (MPa) Critical Temperature (K) Critical Density (kg/m3) Carbon Dioxide(CO 2 ) Pure % Helium % Propane % Air Ethane (C 2 H 6 ) Pure Helium Pure Propane (C 3 H 8 ) Pure Air (78%N 2, 21%O 2, 1%Ar) CYCLES III predicts an almost linear relationship between turbine inlet temperature and net cycle efficiency. Net cycle efficiency refers to the efficiency of the cycle once all losses, including the pumping power of water in the precooler, have been accounted for. The behavior is similar regardless of the pressure drop in the IHX, i.e. the linear relationship between turbine inlet temperature and efficiency holds, but the efficiency falls for higher pressure drops. Figure 2.10 shows the net cycle efficiency of the recompression cycle for an IHX pressure drop of 300 kpa and turbine inlet temperature of 510 o C Turbine Inlet Temperature ( o C) Figure 2.10: The effect of turbine inlet temperature on the cycle operating with pure CO 2, assuming an IHX pressure drop of 300 kpa. The behavior of the cycle at varying turbine inlet temperatures is similar for changing impurity concentrations. For the impurities discussed next, 510 o C was chosen as the constant 38

39 MC Work (MW) RC Work (MW) Net Cycle Efficiency turbine inlet temperature, but the efficiency lost for a given impurity concentration, as compared to the efficiency when running on pure fluid, will be the same regardless of turbine inlet temperature. Figure 2.11 shows the net cycle efficiency when helium impurities are added to the working fluid. No real change is observed until the mole fraction of helium reaches The change in the critical point causes a rise in the main compressor work, as shown in Figure Mole Fraction of He Figure 2.11: The effect of a helium leak detection gas on the S-CO 2 cycle efficiency. About 0.5 mole % He is expected to be needed for leak detection in a large plant Mole Fraction of He Mole Fraction of He Figure 2.12: The compressor work as the helium mole fraction is changed. The main compressor (left) is affected more than the recompressing compressor (right). As the critical point shifts, the main compressor becomes closer and closer to an ideal gas compressor, requiring more work. The recompressing compressor, already further from the critical point, shows less of a change in the work required. It actually requires less work for 39

40 Net Cycle Efficiency (%) compression as the mole fraction of helium is increased, but the decrease in the work of the recompressing compressor is more than offset by the increase in work of the main compressor. It is evident that helium has a detrimental effect on the efficiency of the S-CO 2 recompression cycle. A level of 0.5 mole % helium degrades the efficiency of the representative plant by about 1.0 %. If the cooling water temperature could be decreased commensurate with the critical point, efficiency could be maintained, but that is only realistic to a point and only in colder latitudes Air Impurities Other inevitable impurities will exist, air being the most likely. However, the critical point of helium is so low that if it is present, helium s effects will dominate and any efficiency penalty due to air will be negligible in comparison. It can be assumed that CO 2 used in any operating cycle will be relatively pure, but some air will be present. Unless the fraction of air impurities becomes high, it is expected that little to no effect on efficiency will be observed. Figure 2.13 shows the effect of air impurities on the net cycle efficiency Mole Fraction of Air Figure 2.13: The effect of air impurity on the S-CO 2 cycle. The mole fraction of air in commercially available CO 2 can be or even lower. The effect of air on the cycle is not detrimental at the concentrations expected. Air has no effect on the cycle performance, up to mole fraction and a small negative impact up to mole fractions of about These air concentrations are well above the expected range of air impurities because commercially available CO 2 has purities of 99.8 % and above [Freas, 2007]. Even at an air mole fraction of 0.010, the efficiency penalty is still just

41 %. Therefore, likely levels of air impurities are expected to contribute negligibly to losses in cycle efficiency. 2.5 Chapter Summary The S-CO 2 recompression cycle outperforms other cycles in efficiency terms if operated within certain temperature ranges. Its turbomachinery is markedly more compact, as evidenced in the compressor designs discussed next in Chapter 3. Test recompression cycles have not been built and further work is needed to model these systems. CYCLES III is designed to give accurate calculations for the operation of simple and recompression Brayton cycles at steady state. Its major improvements are the inclusion of the simple cycle and the ability to model fluid impurities, or cycles using any fluid. CYCLES III runs showed that a helium leak detection gas was detrimental to the efficiency of the S-CO 2 cycle, causing a loss of 1.0 % efficiency at a helium mole fraction of If leak detection capability can be proven effective in supercritical CO 2 with a helium mole fraction of less than 0.005, then helium leak detection could be a very appealing feature of the recompression cycle. Air impurities are not as harmful to the cycle and can be tolerated at mole fractions up to with essentially zero loss in efficiency. Expected air impurities have no real effect on cycle efficiency. The ethane simple recuperative cycle shows little promise unless ethane cracking can be maintained at a low mole fraction. This is likely not possible at the high temperatures needed to produce an attractive efficiency. The rate of recombination, and the equilibrium concentration of different hydrocarbons are not known for an ethane cycle, though. Therefore, conclusions about the attractiveness of the cycle cannot be complete until more experimental data is available in the high pressure and high temperature ranges that would be necessary for a PCS. From analysis of the cycle performance with expected dissociation, however, the ethane recuperative cycle appears to have very little real promise. 41

42 2.7 Nomenclature for Chapter 2 D Diameter (m) f Friction factor, main compressor flow fraction k form loss coefficient L Length of pipe (m) m mass flow rate (kg/s) P Pressure (Pa) Re Reynolds number S Maximum allowable stress (Pa) t pipe thickness v flow velocity (m/s) y Safety factor of 0.4 Greek Letters ρ Density (kg/m 3 ) 42

43 3 S-CO 2 Compressor Design 3.1 Introduction CO 2 compressors are used in many industries, but few applications require operation close to the critical point. Carbon sequestration is one area in the electric power production industry that may spawn interest in S-CO 2 compressor design. Presently, however, there is little available information on large-scale S-CO 2 compressors operating near the critical point. Modeling of CO 2 compressors, especially those operating near the critical point, is important to further development of the recompression cycle. 3.2 Developing Compressors for the S-CO 2 Cycle The Need for a Compressor Model Efforts on the part of Tri Trinh have been directed toward modeling of S-CO 2 power conversion systems in transients and tuning controls for the system [Trinh, 2009], but compressor performance in his work was originally based on ideal-gas models adjusted to CO 2 densities. The adjustment consists of scaling compressor work inversely with density. The profound changes in fluid properties near the critical point make this approach less than certain. Also, the reductions in compressor work and in turbomachinery size are some of the main advantages of an S-CO 2 recompression cycle. These factors demand the development of models to design the compressor for the steady state design point and to model the off-design performance of S-CO 2 compressors. Centrifugal compressors are the first choice for the recompression cycle because they are durable, have larger margin to surge than axial compressors, and are expected to perform well based on the operating parameters of the S-CO 2 cycle. The Real Gas Radial Compressor (RGRC) code was developed in this work for the purpose of sizing and modeling the performance of S-CO 2 centrifugal compressors Compressor Background There are many types of industrial compressors, including axial, positive displacement, and centrifugal (a.k.a. radial) compressors. All compressors can be described by a set of nondimensional numbers. These are specific speed, flow coefficient, and head coefficient [Japikse, 1994]. They are defined as 43

44 Specific Speed, Flow coefficient, Head coefficient, Ns = Ω V φ = ψ = (gh) 3 4 Eqn. 3-1 m Eqn. 3-2 ρωd3 ΔP ρω 2 Eqn. 3-3 D2 where D is the outlet diameter of the impeller, Ω is the rotational speed in revolutions per second, V is the volumetric flow rate at the inlet, g is the acceleration of gravity, H is the adiabatic head (in units of length), m is the mass flow rate, and ρ is the density at the impeller inlet in consistent units. Using these parameters, a designer can select the type of compressor appropriate for a given application. Figure 3.1 shows the range of applicability for a few different compressor types. In industry practice it is common to encounter non-dimensional parameters that retain many Imperial units. For these cases, volumetric flow is in gallons per minute, rotational speed is in RPM, and head is in feet. The result is that a truly non-dimensional specific speed will be equal to 1/129 the value obtained with Imperial units. Care should be taken to examine the unit system for specific speed calculations, as the Imperial unit system is not the only one used in industry. 44

45 Figure 3.1: Design ranges for different compressor types. Lines of constant specific speed are labeled. Centrifugal compressors are appropriate in Region A, Axial compressors in Region B, and Reciprocating compressors in Region C. Other compressor designs are used in other regions of this plot. Adapted from Japikse [1994]. In the S-CO 2 recompression cycle, centrifugal compressors are the most appropriate, based on experience with the non-dimensional parameters. Every design discussed here will assume a rotational speed of 3600 RPM at the design point, in order to synchronize the shaft with the electric grid. Looking at the equation for specific speed, it becomes clear that, to achieve good performance, smaller machines should be built with higher rotational speeds or lower stage pressure ratios. For example, the small test compressor operated by Sandia National Laboratory has a mass flow rate of only 3.53 kg/s at the design point. With a pressure ratio of about 1.8, this requires that the compressor be operated at speeds of 65,000 to 75,000 RPM [Wright et al., 2008]. Tables 3.1 and 3.2 show the operating points and non-dimensional parameters characteristic of a recompression cycle design of 500 MWth. This cycle is identical to the recompression cycle discussed in Chapter 2. 45

46 Table 3.1: The operating points of the compressors in the recompression cycle. The recompressing compressor is assumed to be a two-stage design. Inlet Outlet Stage Mass Flow Pressure Temperature Pressure Temperature Rate (kg/s) (MPa) ( o C) (MPa) ( o C) Main Recomp Stage Stage Table 3.2: The non-dimensional parameters of the compressors in the recompression cycle. The two stages of the recompressing compressor are shown separately. Mcomp Recomp 1 Recomp 2 Sandia Test Specific Speed Ns Head Coefficient Ψ 1.917E E E E-3 Flow Coefficient φ 9.80E E E E-03 Based on the non-dimensional parameters given in Table 3.2, the centrifugal compressor is the best choice for the S-CO 2 recompressing compressor. The values of the non-dimensional parameters given in Table 3.2 are extreme values in the centrifugal compressor range. They do not match Figure 3.1 but the centrifugal compressor is a better option than any other based on Figure 3.1. The values for the Sandia test compressor are based on a rotational speed of 45,000 RPM. The Sandia test compressor comes closer to the centrifugal compressor region in Figure 3.1. The recompression cycle s main compressor can be designed as a single stage for a PCS rated above ~400 MWth and a two-stage design is best suited for the recompressing compressor. If the PCS power is reduced below 400 MWth, the mass flow rates of the compressors are reduced. In order for the specific speed of each stage to remain within the range of centrifugal compressors, the pressure ratio of each stage must be reduced, and therefore the number of stages must be increased. In order to produce a design of only one stage for the main compressor, the cycle power must be above 400 MWth. To understand the operation of a compressor design code a few centrifugal compressor concepts will be necessary. First, terminology is necessary to understanding. Figure 3.2 shows several parts of a centrifugal compressor. The view given in Figure 3.2 is termed the meridional plane. It is defined as the plane that contains the axis of rotation. 46

47 Figure 3.2: The meridional plane view of a typical centrifugal compressor. This exaggerated view is probably not to scale for any real compressor design. Flow enters at the impeller inlet, sometimes called the inducer. The term inducer identifies the portion of the rotor whose blade passage is at the inlet, before radius has begun to increase. The impeller turns along the axis, and flow exits the impeller into a vaneless space. Sometimes the vaneless space is formed with two parallel plates and sometimes the plates diverge. In the Real Gas Radial Compressor (RGRC) code, the vaneless space is always of constant depth in the axial direction. Beyond the vaneless space is typically a vaned diffuser, which serves to slow down the flow and raise the static pressure of the fluid. It is a circular plate of metal that has vanes inside it which direct the flow, such that the flow area of the passage increases as radius increases. Figure 3.3 shows a view of a straight-vaned diffuser looking along the axis of rotation. In RGRC the vanes can be curved by the user up to 25 o. This just means that the angle of the vane with respect to the radial direction will be 25 o greater at the diffuser outlet than it is at the diffuser inlet. The area ratio of a diffuser refers to the ratio of the outlet flow area to the throat flow area. 47

48 Figure 3.3: A straight vaned diffuser. These vanes are of width 8 o and there are twenty of them. They are inclined at 70 o to the radial direction. After the vaned diffuser is a scroll, or volute, which collects the flow and directs it to the next component of the system. In a multi-stage compressor the vaned diffuser of upstream stages will be followed instead by a return channel which collects the flow and directs it to the next stage. The volute is neglected in RGRC because its design will depend on available space and material. In the multi-stage performance code, the return channel is treated as a form loss with a form loss coefficient chosen by the user. The casing refers to the static portion of the compressor which surrounds the impeller. In shrouded impellers, the blade passage is completely enclosed from hub to shroud. Unshrouded impellers, like those in RGRC, have blade passages which are open at the tips of the blades. This produces some losses which will be discussed later. Compressors operate between two limits: surge and choke. At low mass flow rates, compressors stall or surge depending on the phenomenon exhibited. Both are limiting conditions. Stall occurs when the flow experiences separation of the boundary layer on blades or in narrow passages. Stalled portions of the flow develop and form stall cells. Sometimes the cells will rotate through the compressor in what is aptly called rotating stall. RGRC neglects these phenomena and simply states that stall is likely to have occurred. Surge, the other phenomenon which occurs at low mass flow rates, results in reversal of the flow and can cause violent vibrations. The operating range of a compressor is bounded at low mass flow rates by what is termed the surge line, as shown in the example compressor map of Figure 3.4. The operating limit at low mass flow rates is termed the surge line by convention, whether the actual phenomenon occurring is surge or stall. In practice, the surge line occurs where the slope of the 48

49 pressure ratio curve is zero. An operator will likely find that the surge line in RGRC occurs at higher mass flows than the zero slope condition, due to the many conditions that the code will identify as surge/stall. These conditions are believed to be conservative estimates because none of these criteria has been seen to be sufficient to predict surge in experiments. Figure 3.4: Example compressor performance map showing the relationship between the surge points for different speeds (in % of design speed) in a typical centrifugal compressor. At high mass flow rates, regions of the flow will become supersonic, resulting in severely deteriorating performance at high mass flow rates. Choke is assumed to occur when the ratio of the core flow velocity is greater than 90 % of the critical velocity. A note should be made about calculating the critical velocity. The critical velocity will always be different than the speed of sound and will always be smaller. Critical velocity is defined as the velocity that must be chosen to achieve supersonic flow for a constant value of stagnation enthalpy. Critical velocity is therefore a function of stagnation enthalpy whereas the speed of sound is a function of static enthalpy. Appendix B discusses the development of the critical velocity database. At each point in the calculation of compressor performance, the core flow velocity is compared to the critical velocity to test for choke. The Euler turbomachinery equation describes the fundamental cause of pressure rise in a compressor. By imparting rotation to the fluid, the total enthalpy of the fluid is increased. The rise in static enthalpy through the impeller is given by [Cumpsty, 2004] 2,st 1,st = 1 2 U 2 2 U W 1 2 W 2 2 Eqn

50 where h 2,st and h 1,st represent the static enthalpies of the fluid at the impeller inlet and outlet respectively. The letter U represents blade speed and W is the relative speed of the fluid. Subscripts indicate inlet at the Root Mean Square (RMS) radius (1) or outlet (2). The Euler turbomachinery equation is used directly in RGRC to calculate the static enthalpy rise produced by the impeller. Further rise in static enthalpy is achieved by pressure recovery in diffusers, where the dynamic pressure, ½ρv 2, is reduced and static pressure rises as the flow area expands. Mean-line codes treat the flow in a compressor by modeling the behavior of the fluid at the mean streamline, the surface along the RMS radius of the blade passage. Mean-line compressor codes can be used to develop initial sizing, design, and performance estimates for compressors. In fact, these methods are typically more accurate for determining off-design performance than more advanced computational fluid dynamics (CFD) codes due to their empirical nature [Aungier, 2000]. The mean stream line method was used to improve on existing compressor codes to achieve some understanding of how compressors will perform in an S-CO 2 recompression cycle. Existing codes available to MIT did not produce results consistent with themselves and they were very difficult to use and manipulate. These codes were adjusted NASA codes known as CCD and CCODP, which had been altered to work for supercritical CO 2. The code structure made editing very tricky. Several remaining ideal-gas assumptions were not appropriate for a real gas compressor. These assumptions persisted despite the fact that real gas property subroutines were included in the codes. Therefore, effort was needed to produce an improved mean-line real gas compressor code. 3.3 Real Gas Radial Compressor (RGRC) Code Issues with Earlier Codes CCDS/CCODS and Motivation for RGRC Development The NASA mean line centrifugal compressor codes were adjusted by Yifang Gong of the MIT Gas Turbine Laboratory (GTL) to operate with CO 2 near the critical point [Hejzlar et al., 2007] These codes consisted of a design code, CCD, and an off-design code, CCODP. They had originally been developed at the NACA Lewis Flight Laboratory, primarily by Jerry Wood [Wood, 1995]. After updates for S-CO 2 by Gong, they were renamed CCDS and CCODS, with the S added for S-CO 2. The CCD/CCODP input data requires the user to choose some basic parameters, but most of the geometry of the compressor is determined by the code in a complicated iterative process. The NASA codes rely on correlations and experimental diffuser data for air and its calculations 50

51 Density (kg/m 3 ) are based on a constant value for the ratio of specific heats, C p /C v. For diffuser performance the NASA codes used Runstadler s database of diffuser performance [Runstadler, 1969]. This database is one of the most thorough available, but it was determined that the data were not realistic for S-CO 2. For Supercritical CO 2 the ratio of specific heats and other properties change dramatically near the critical point, so Gong s changes were focused on developing a set of polynomials for determining fluid properties for S-CO 2 and implementing those subroutines within the existing NASA codes. He succeeded in producing a set of polynomials that run very efficiently for the range of fluid properties that is of interest to recompression cycles. Figure 3.5 shows Gong s subroutines compared with REFPROP results. In the range of interest for the recompression cycle, Gong s polynomials produce very good results and are able to do so quickly J/kgK : Gong 1350 J/kgK : NIST 1450 J/kgK : Gong 1450 J/kgK : NIST 1550 J/kgK : Gong 1550 J/kgK : NIST Enthalpy (kj/kg) Figure 3.5: Fast-running fluid property subroutines for S-CO 2 produced by Gong, as they compare to NIST REFPROP values. Density is plotted against enthalpy for three lines of constant entropy: 1350 J/kgK, 1450 J/kgK, and 1550 J/kgK as indicated in the legend to the right. Each entropy line has a value of enthalpy above which Gong s subroutines are not applicable. It is evident in Figure 3.5 that both property subroutines have their limitations. At very low enthalpy, the REFPROP subroutines return errors, and at higher enthalpies, Gong s subroutines deviate from the REFPROP subroutines. For recompression cycles, however, Gong s subroutines perform well. Figure 3.6 shows the range of applicability for Gong s subroutines. 51

52 Density (kg/m 3 ) Enthalpy (kj/kg) Figure 3.6: Range of Applicability for Gong s S-CO 2 property subroutines Figure 3-5 shows the density as a function of enthalpy for three lines of constant entropy. By drawing a line through the points where the property routines diverge, an expression for the range of validity for Gong s subroutines was developed. If the density at the impeller outlet falls outside the range bounded by the two lines in Figure 3.6, RGRC will return a warning to the user that the fluid property subroutines cannot be trusted in that range. On the whole, Gong s fluid property subroutines are quite successful. They reduce the computing time for many calculations by orders of magnitude. Subroutines calling Gong s polynomials were substituted for the calculations already present in CCD and CCODP. In principle, these changes should have been enough to produce basic compressor designs and performance maps. The structure of the code and its variable naming scheme were left unchanged by Gong. CCD and CCODP are written in Fortran 77, using almost no subroutines and scores of GO TO statements. The code is very difficult to understand for these and other reasons. Furthermore, there were large disagreements between the design code and the off-design code when run on CO 2. Part of the problem was inconsistency in Gong s application of his new property subroutines. The performance maps did not agree with the design code, sometimes showing as much as 20% difference in the stage pressure ratio for the design point. An example of the discrepancies is shown in Figure 3.7. The pressure ratio graph shows a vertical surge line, a feature never observed in real compressors. The effect is produced by CCODS because no surge criterion has been met. Instead, the surge line in Figure 3.7 only serves to indicate the mass flow rate at which calculations begin. 52

53 Total-to-Static Efficiency Total-to-Static Pressure Ratio % 90% 80% 70% 60% Mass Flow Rate (kg/s) % 90% 80% 70% 60% Mass Flow Rate (kg/s) Figure 3.7: A single-stage main compressor map from CCODS showing unusual features. The pressure ratio (top) shows that surge occurs at the same mass flow rate regardless of speed and the design point does not appear at all. The design point is 3600 RPM and kg/s. Speeds are in percent of design speed Also, the off-design code was not self-consistent if the speeds for the compressor map were changed by the user. The source of this error was never discovered. Evidently, there were some data being preserved as calculations proceeded from one compressor speed to the next, but the complexity of the code made it impossible to diagnose the problem. CCDS and CCODS develop a compressor design based on some methods which were not advantageous because of inconsistencies in the results and difficulties involved in using the code for power producing S-CO 2 cycles. First, CCDS develops a compressor design based on an input value of specific speed. The choice of specific speed as an input unnecessarily complicates the code when it is used for compressors in electricity production. Presumably the choice of input specific speed was made because specific speed is used to characterize compressors based on their application. The code used the input value of specific speed to calculate a value for 53

54 RPM. In the case of electricity production, the compressor will be operating at 3600 RPM or some fraction of 3600 RPM, so it was desirable to input RPM and avoid the complications of specific speed. Choosing a specific speed meant that the designer would have a more difficult process than if the rotational speed was an input. CCDS also required an input value of the de Haller number, the ratio of relative velocity at impeller inlet to that at the outlet, W2OW1T in CCDS/CCODS. This limit was intended to allow the user to guarantee a design that would meet the criterion of W 2 /W 1 > de Haller introduced this criterion as a way of guaranteeing that the stage would avoid stall, but this method is not entirely sufficient [Cumpsty, 2004]. The de Haller number is a limit on the head loading of each stage in a multi-stage compressor. In other words, it is a limit on the pressure ratio for a single stage. Therefore, a low de Haller number should be an indication to the designer that a compressor design needs to be reevaluated in terms of stage number. The constraint resulted in some unphysical results. By restricting the relative velocities to be proportioned by the designer, the mass flow rate at impeller outlet did not match that at impeller inlet in every design. The difference could be as much at 5.6 % in CCDS. Furthermore, the constraint in the outlet velocity meant that the calculated enthalpy and pressure rise were not reliable. The outlet velocity triangle was calculated based on an assumed relationship to the inlet triangle and the proportional relationship between outlet diameter and blade speed. The above shortcomings prompted an effort to produce a new code that would take advantage of Fortran 90 s improvements and would be accurate, user-friendly and more readable for new users. The new code s compressor maps agree with the design point and there is a supplement that allows stages to be coupled into a multistage design (up to three stages). It has been named RGRC, for Real Gas Radial Compressor, and the multistage code has been called RGRCMS, with the MS added for Multi-Stage Basic Outline of the RGRC Code Designing compressors is sometimes described as a combined art and science. Some parameters of the design must be known by the designer in order to achieve acceptable performance. Some geometrical parameters are determined within RGRC in order to alleviate some decision-making on the part of a code user who may be inexperienced with compressors. However, the designer must make many important choices about compressor parameters in order to achieve a successful design. The code will return warnings to the designer to indicate what parameters can be changed in order to avoid problems. The code calculates all quantities based on physical laws, experimental correlations, and experimentally determined fluid properties. The code can be broken into several portions. They are: 54

55 1. The Impeller Inlet (Inducer) 2. Dimensioning the impeller 3. The Impeller Outlet 4. Losses 5. The Vaneless Space 6. The Vaned Diffuser After the design portion is complete, the off-design performance is computed by repeating the above list (with the exception of item 2) for a range of impeller speeds and mass flow rates Variable Nomenclature There is a consistent naming scheme to the variables in the code. Numbers 0 through 4 are used to denote positions in the compressor beginning from inlet and going to outlet. 0- Conditions upstream of the compressor 1- Inducer inlet 2- Impeller outlet 3- Vaned Diffuser Inlet 4- Vaned Diffuser Outlet Absolute velocities are designated with a V, relative velocities with a W, and blade speeds with a U. At the inducer inlet a T denotes the blade tip, H the hub, and MF the root mean square radius. A U or M for tangential and meridional, respectively, will appear as the second letter in velocity components. For example, VU1MF is the tangential component of the absolute velocity at the RMS radius of the inducer inlet. Simpler examples include U1T and U2: the blade tip speeds at inducer inlet and impeller outlet, respectively. The blade tip speed at the impeller outlet (2) does not have a tip and a hub speed because they are equivalent when the blade passage is oriented perpendicular to the rotating axis as at the impeller outlet. Enthalpies, densities, and pressures are saved as structured data types of total, stat, and rel, such that P3.stat is used for the static pressure at position 3, H1.rel is the relative enthalpy at position 1, and H2.total denotes the total enthalpy at position Impeller Calculations The impeller inlet dimensions are determined from a few inputs from the user. These include hub diameter and the fluid properties upstream of the compressor, including mass flow rate, static pressure, entropy and velocity. RGRC always assumes a zero prewhirl condition, because the design of the inlet guide vanes will depend on many things external to the compressor and will be important for transient control of the cycle as a whole. Prewhirl, however, can be very 55

56 important to the performance of a centrifugal compressor. Hub diameter will be determined by the diameter of the shaft and whether or not the shaft must protrude through the hub (as in a multistage design, for example). This determination will have to be made by the user, considering torque, materials and the configuration of the system. The code uses the input parameters to determine the diameter of the blade tips that the impeller must have in order to accommodate the design mass flow rate at the inlet, given the velocity and density of the fluid. The calculation is among the most simple in the entire code, basing inducer size on the mass flow rate, the designer s chosen number of blades and the dimension for blade thickness. Inducer blade tip diameter is determined by π 4 D 1T 2 π 4 D 1H 2 Z 1 (D 1T D 1H )t LE = m Eqn. 3-5 ρv 1 where D 1T is the tip diameter, D 1H is the hub diameter, Z 1 is the number of blades, t LE is the leading edge thickness of the blades and V 1 is the inlet velocity at the RMS radius. This is just a statement of conservation of mass. These calculations are contained in the subroutine INLET and the velocity triangle is computed in the subroutine INLET_TRI. To calculate the velocity triangle at the outlet, a phenomenon known as slip must be understood. The meridional plane is defined in centrifugal compressor design as the plane that contains the axis of rotation. At the inducer, the meridional direction is the same as the axial direction and at the impeller outlet, it is equivalent to the radial direction. Based on conservation of mass as the flow progresses in the meridional direction, the velocity triangle at impeller outlet can be determined. Observed impeller performance, however, reveals that the flow slips as shown in Figure 3.8. Slip is the result of pressure gradients at the blade passage outlet and is explained in more detail in [Cumpsty, 2004]. 56

57 Figure 3.8: The velocity triangles at impeller inlet (above) and outlet (below). The Weisner slip correlation [Cumpsty, 2004] is used to determine the slip velocity and from that, the impeller outlet velocity triangle. The slip velocity is given by V slip = U 2 χ 2, Eqn. 3-6 (Z 2 ) 0.7 where χ 2 is the blade angle at outlet, Z 2 is the number of blades at outlet, and U 2 is the blade speed at outlet. The ideal case assumes that the relative flow at impeller outlet will be at an angle of zero to the blades. In other words, the ideal relative flow angle (angle from meridional) is equal to the blade backsweep angle χ 2. Figure 3.9 shows the backsweep angle on a schematic impeller. 57

58 Figure 3.9: A simplified schematic of an impeller showing the definition of backsweep angle, χ 2. Backsweep angle in RGRC is measured with respect to the radial direction. With the ability to calculate the impeller outlet velocity triangle, the code first assumes an outlet diameter based on a ratio of inlet tip to outlet diameter, which is an input from the user. Within the code, this ratio is called LAMX. This ratio is typically between 0.3 and 0.5 for a centrifugal compressor impeller. LAMX = D 1T D 2 Eqn. 3-7 If this ratio is too high, the impeller will begin to resemble an axial machine, but the flow through it will not benefit from the blade shape. Therefore, there will be a decrease in fluid density through the impeller. In other words, if the diameter ratio is initially too high, then the machine will not compress the fluid at all. In this case, the code will alert the user to choose a lower starting value for the diameter ratio. With the first value of the impeller outlet diameter chosen, the code begins by assuming a density value slightly higher than the impeller inlet density. Using this value, the slip correlation, and the conservation of mass requirement, the code will calculate the velocity triangle at outlet. The key relationships are determined as described in Figure 3.8. The mass flow rate relation is defined by W 1 W 2 = ρ 2A 2 ρ 1 A 1 Eqn. 3-8 A 2 = πd 2 b 2 Z 2 b 2 t TE cosχ 2 Eqn

59 A 1 = π 4 D 1T 2 2 D 1H cosβ 1 Eqn Here, W 2 is the ideal relative velocity at impeller outlet, because outlet flow area A 2 is defined by the backsweep angle. The relative velocity at the inlet, W 1, represents the value at the RMS radius. The true relative velocity at the outlet is determined with the slip correlation described previously. Once the velocity triangle is determined, the enthalpy rise is calculated using the Euler turbomachinery equation. This enthalpy rise is then used to determine a new value for the fluid density at the outlet by calling the property subroutines with the calculated enthalpy as an input. The new value of density is then used to repeat the calculation until the density of the fluid converges. These calculations are contained in the subroutine OUTLET. Once the density converges, the velocity triangle and enthalpy rise are known for the current impeller outlet diameter. The process of determining the impeller s performance is shown in Figure The impeller will not be resized in the design portion of the code until the diffuser outlet static pressure is known, and therefore the entire compressor performance can be compared to the desired performance. Figure 3.10: The process for determining impeller performance. The outlet conditions of the impeller rely on the convergence of fluid density. Mass conservation determines the outlet triangle for each density iteration. 59

60 3.3.5 Loss Calculations Within the impeller losses will occur. They are represented by both pressure losses and additional work terms. The loss calculations depend on some parameters that describe the shape of the impeller. The impeller shape is determined by the hub and tip diameters at inlet, the outlet diameters, blade height, and blade angles. The shape will affect the losses as the fluid flows through the passages. The subroutine IMP_SHAPE calculates the blade length based on the impeller diameters and the blade angles. The blade passage is assumed to follow an elliptical shape in the meridional plane. The impeller losses are then calculated using subroutines that are based on empirical or semi-empirical formulas. There is no hard and fast convention for how losses are calculated. When more experimental data for S-CO 2 compressors is available in the literature, the loss calculations may be improved by adding appropriate correction factors to the present loss correlations. Losses in the impeller are subdivided into incidence, blade loading, skin friction, hub-toshroud loading, mixing, diffusion, expansion, and tip clearance loss. These are expressed as fractional pressure losses and are defined as described by Aungier [2000]. Disk friction, leakage, and recirculation losses are expressed as additional work terms, per unit mass. The total fractional pressure loss, ω tot, will be converted into an absolute pressure loss by P imp = ρ 1V 1 2 ω tot 2 Eqn so that ω tot represents a portion of the dynamic pressure at the impeller inlet. Clearance loss is the loss associated with Coriolis forces on the fluid between the impeller blades and the stationary casing. It is defined as a fractional pressure loss and is given by ω CL = 2m CL P CL m ρ 1 W 1 Eqn where P CL is the pressure gradient along the clearance gap and is determined by the geometry of the impeller blades, the blade speeds, and the mass flow rate through the impeller, as P CL = m D 2V U2 D 1 V U1 2 Z eff r b L b Eqn

61 where r and b are the average passage radius from the axis of rotation and the average passage height from hub to shroud, respectively. The clearance mass flow rate is a function of the blade geometry and flow rate. m CL = ρ 2 U CL Z eff L b b CL Eqn where b CL is the blade to shroud clearance and U CL is an empirical clearance flow velocity, given by U CL = ABS(2 P CL /ρ 2 ) Eqn Skin Friction is the loss associated with the shear forces of the flow against the surfaces of the impeller and the casing. It is defined as a fractional pressure loss and is given by ω SF = 4C ft W rms W 1,mf 2 Lb D yd Eqn where W rms is the RMS value of relative velocity from impeller inlet to impeller outlet, given by W rms = 1 2 W W 2 2 1/2 Eqn The turbulent skin friction factor, C ft, is given by C ft = C fts Re e < 60 C fts + C ftr C fts 1 60/Re e Re e 60 Eqn where Re e is a Reynolds number which takes into account the roughness of the surface. It is used only to define the friction factors and is defined as Re e = Re d 2,000 e D yd Eqn where e is the surface roughness, Re d is the Reynolds number based on average hydraulic diameter, and D hyd is the average hydraulic diameter of the impeller passage. The additional subscripts s and r refer to the smooth surface and rough surface friction factors. The roughness effect becomes important when Re e is greater than 60. The friction factors are given 61

62 in Eqn and The smooth surface friction factor must be solved iteratively. It depends only on the Reynolds number based on hydraulic diameter. 1 4C fts = 2log Re d 4C fts Eqn The rough surface friction factor depends on the hydraulic diameter and the average surface roughness, e. 1 4C ftr = 2log 10 e 3.71D yd Eqn Blade loading loss, or diffusion blading loss, is the loss associated with buildup of the boundary layer inside the blade passage. It reflects the increase of the boundary layer thickness and the separation of the flow caused by pressure gradients within the passage. Blade loading loss is defined as a fractional pressure loss and can be calculated by ω BL = ΔW/W Eqn where ΔW is a velocity representing the increase in loading from the impeller inlet to the outlet. It is given by ΔW = 2πD 2(dH aero ) Z eff L b U 2 Eqn where Z eff is the effective number of blades, taking into account that splitter blades of half the length of the full blades may be used in some impellers. The effective blade number is given by Z eff = Z 1 + Z 2 Z 1 L split L b Eqn where L split is the length of splitter blades and dh aero is the total aerodynamic enthalpy rise in the impeller. The total aerodynamic enthalpy rise is defined by the velocity triangles calculated in OUTLET. The ideal aerodynamic head is equal to dh aero less the enthalpy change attributable to losses. 62

63 The incidence loss is the loss associated with redirection of the flow when it makes contact with the inducer blades. The incidence loss should be a minimum at the design point. Negative or positive incidence upon the inducer will result in a greater loss. Incidence loss is defined as a fractional pressure loss and is given by ω INC = V 1 / W 1 sinβ Z 1 t LE / πd 1 sinβ 1 2 Eqn Recirculation loss is caused by recirculation of the flow at the impeller outlet. It is caused by mixing of the wake at the impeller blade tip and is greater when there is backflow to the impeller. Recirculation loss is defined as a total work addition and can be calculated by I RC = D eq 2 1 W U2 V M2 2cotβ 2 Eqn D eq = W max /W 2 Eqn where D eq is the equivalent diffusion factor. The equivalent diffusion factor takes into account the change in relative velocity from the impeller inlet to the outlet. The relative velocity W max is a function of the inlet and outlet velocity triangles and ΔW which was defined earlier in Eqn W max = W 1 + W 2 + ΔW /2 Eqn The mixing loss is caused by mixing of the flow at the impeller outlet and is modeled similar to an abrupt expansion loss. It depends on a wake velocity, C m,wake, and a mixing velocity, C m,mix. The mixing loss is defined as a fractional pressure loss. ω MIX = C m,wake C m,mix /W 1 2 Eqn The wake velocity is a function of the blades speed and a separation velocity, W SEP, which depends upon the recirculation of the flow. 2 2 C m,wake = W SEP W U,1 Eqn

64 W SEP = 0.5W 2 D eq if D eq > 2.0 W 2 if D eq < 2.0 Eqn Where D eq is the equivalent diffusion factor as defined earlier in Eqn The mixing velocity simply takes into account the flow expansion at the impeller outlet, and is therefore a function of the flow velocity and the blade passage geometry at the outlet. C m,mix = V 2 A 2 / πd 2 b 2 Eqn Diffusion losses are those losses which occur between the leading edge of the impeller blade and the blade passage throat. They are negligible for most impellers and are rarely greater than the blade incidence loss. The diffusion loss is defined as a fractional pressure loss. ω DIF = W t /W 1 2 ω INC Eqn where W t is the relative velocity without the inlet blockage considered. The diffusion loss must be greater than zero. If the calculated value is negative it will be set to zero. Hub-to-shroud mixing losses are caused by the pressure gradient between the hub and the shroud, within the blade passage. The hub-to-shroud mixing loss is defined as a fractional pressure loss. ω HS = κ m bw/w 1 2 /6 Eqn κ m = α 2 α 1 /L b Eqn and b and Ware the average blade passage height and relative velocities, respectively. Within the blade passage there is an expansion loss caused by imperfect diffusion through the expanding blade passage. The result depends on the blockage at the impeller outlet which is determined by correlation to be B 2 = ω SF ρ 1V 1 2 ρ 2 V 2 2 W 1D yd b 2 A 2 W 2 b 2 2 L b 2 A 1 2 ρ 2 b 2 ρ 1 L b + b clear 2b 2 Eqn and the expansion loss is defined as a fractional pressure loss given by 64

65 ω EXP = 1 1 B 2 1 V M2 W 1 2 Eqn The disk friction loss is caused by frictional torque on the back surface of the disk. Other losses, in bearings, seals, and gear boxes, are combined with the disk friction loss. Disk Friction and windage are defined as a total work addition, given by I DF = C MD + C MC ρ 2 U 2 R 2 2 / 2m Eqn where C MD and C MC are experimentally determined constants related to the blade passage geometry, the velocities, and the Reynolds number of the flow. C MD = 0.75C M Eqn C MC = L b C M 1 D 1T D2 Eqn R 2 R 1T 2 C M0 1 V U2 U C M = 2 1 V 2 Eqn U1 U 1T C M0 = C Ms + C Mr C Ms log Re/Re s log Re r /Re s Eqn C Ms = MAX 2π s/r Re 3.7 s/r 0.1 Re 0.08 s/r 1/6 Re 1/ s/r 0.1 Re 0.2 Eqn C Mr = 3.8log 10 r/e 2.4 s/r Eqn

66 Roughness becomes important at Reynolds numbers greater than Re s, which is defined in terms of the constant C M and the surface roughness ,100 e/r Re s = Eqn C M Re r = 1,100 r/e 6x10 6 Eqn Leakage Loss is defined as a total work addition, given by I Leak = m CLU CL 2U 2 m Eqn where U CL is the same clearance flow velocity used in the clearance loss calculation and m CL is the leakage mass flow rate also required in the clearance loss calculation. Disk friction, recirculation, and leakage loss are calculated as additional work inputs to the system. All other losses are calculated as fractional pressure drops. Once all the pressure drops are known, they are summed and the fluid pressure at the impeller outlet is calculated. The loss of pressure corresponds to a loss in fluid enthalpy, which is calculated using the fluid property subroutines. Once the losses are calculated, the entropy of the fluid is updated, by making the approximation that the increase in entropy is given by ds = d T Eqn where dh is the loss in enthalpy and T is the static temperature of the fluid at the impeller inlet. This approximation results is based on only about a 10 % change in temperature through the compressor stage, so as long as the losses are accurate, the change in entropy should be within 10 % of the correct value. Since the increase in entropy is small compared to the absolute value of the entropy (less than 3 %) the approximation produces very small errors in the state-point of the compressor outlet. The impeller efficiency is determined from all of the actual energy input to the fluid over the total energy input. Impeller efficiency is given by 66

67 η R = dh aero d dh aero + I Leak + I RC + I DF Eqn Vaneless Space and Diffuser Calculations The vaneless space is modeled by assuming conservation of angular momentum and the expansion of the turbulent boundary layer along the walls of the vaneless space. By conservation of angular momentum, rv θ is a constant and rv r is a constant. Thus, the flow angle with respect to the radial direction remains constant with the exception of changes in radial velocity resulting from narrowing or widening of the space. Figure 3.11 shows the flow path through the vaneless space. Due to the conservation requirements, the flow follows a curved path through the space. Figure 3.11: The flow path in the vaneless space (not to scale). The flow angle with respect to the radial direction, α, is a constant. In real compressors the velocity profile at the impeller outlet is highly non-uniform. For that reason the core flow and the flow near the walls will follow very different flow paths. Near the wall, flow can re-enter the impeller and therefore an additional surge condition is used. If the tangent of the absolute flow angle is above 4.0, then the flow is said to be surged. The subroutine VANELESS begins by setting a time step such that the flow will travel 1/500 of the distance to the vaned diffuser in the first time step. That same time step is then used throughout the vaneless space. The velocity and flow direction at the beginning of the time step are assigned to the entire time step. The position of a fluid particle at the end of that time step is then computed. The velocity is computed at the new position, based on conservation of angular momentum, and then the code continues until the position has reached the entrance to the vaned diffuser. Figure 3.11 is not accurate in that it shows a constant angle θ between time steps. In RGRC the angular distance traveled each step will actually decrease, as the velocity decreases. 67

68 For CO 2, the kinematic viscosity is so low that the buildup of the boundary layer in the vaneless space is negligible. The blockage calculated at the impeller outlet is assumed to represent the blockage at the diffuser inlet. The diffuser is modeled very simply as an increase in area, with corresponding losses due to friction, incidence, and mixing of the wake at the outlet. A database of diffuser performance by Runstadler contains the most thorough data on diffuser performance and was used as the diffuser model in the NASA codes [Runstadler, 1969]. However, its use for a real gas resulted in unphysical results. Thus, it was abandoned in favor of a simple model. Diffusers are always vaned diffusers in RGRC. Pipe diffusers are more expensive to manufacture and are covered by a Pratt and Whitney patent [Cumpsty, 2004]. The subroutine AUNGIER will create a vaned diffuser according to the area ratio input by the user and it will orient the vanes such that the incidence angle for the core flow is zero at the design point. It has been named for the source of the diffuser model [Aungier, 2000]. The vanes can be straight or curved. They will be in line with the flow at the design point at position 3 and can curve up to 25 o further at position 4. The vaned diffuser performance is based on the area ratio, which is described by diffuser inlet and outlet passage widths. The axial dimension of the vaned diffuser does not change in RGRC, so the area ratio is the same as the ratio of the arc lengths at the diffuser inlet and outlet. The diffuser performance is calculated by assuming that the flow follows the blade angle at position 4. By calculating the blockage at position 4 and the losses within the diffuser passage, the code iterates the velocity at position 4 until it achieves conservation of mass from position 3 to position 4. The initial guess of the velocity at position 4 is based simply on the area ratio of the vane, but changes in density and blockage cause this value to be incorrect. The blockage at position 4 is calculated as a portion of the flow area by where V R is given by B 4 = K 1 + K 2 V R 2 1 L vane w 4 Eqn V R = 1 2 V M3 sinβ 4 V M4 sinβ Eqn and K 1 and K 2 are empirical constants determined from the diffuser divergence angle, θ C, and the blade loading parameter, L. These are defined in terms of the average blade-to-blade velocity difference, ΔV. K 1 = /C L C θ Eqn

69 K 2 = 2θ C 125C θ 1 2θ C 22C θ Eqn The average blade-to-blade velocity difference is a function of the number of vanes, Z, the length of the vanes, the radius of the diffuser at inlet and outlet and the velocity of the core flow at each position. It is defined as ΔV = 2π R 3V U3 R 4 V U4 ZL vane Eqn and the defining correction coefficients for blade loading and divergence angle are given by 1 C L = 2θ C /11 Eqn C θ = 3L Eqn where the diffuser divergence angle is defined as θ C = tan 1 (w 4 t b4 w 3 + t b3 )/(2L vane ) Eqn and the blade loading parameter is defined as L = ΔV V 3 V 4 Eqn Losses within the vaned diffuser are divided into a skin friction loss, an incidence loss, and a wake mixing loss. The skin friction loss is defined as a fractional pressure loss and is given by ω SF = 4c f V/V 2 3 L vane, Eqn d H (2δ/d H ) 0.25 where the skin friction coefficient is calculated just as it is in the impeller. The hydraulic diameter is the average of the hydraulic diameters from the diffuser inlet and outlet. The boundary layer thickness, δ, is given by 2δ d H = 5.142C ft L vane d H, Eqn

70 which is a flat plate approximation. The boundary layer thickness is restricted to be less than or equal to one half the hydraulic diameter. Incidence loss upon the diffuser vane depends upon the incidence angle relative to the vane angle. ω INC = 0.8 (V 3 V 3 )/V 3 2 Eqn where V 3 is the throat velocity at the design point. The diffuser wake will experience a mixing loss as the flow slows from the wake velocity to the mixed velocity. The mixing loss is calculated similar to that of the impeller. It depends on a mixing velocity and a wake velocity at the diffuser outlet. ω MIX = V M,wake V M,mix /V 3 2 Eqn The wake velocity again depends on the separation velocity and the tangential component of the flow velocity at the diffuser outlet. V M,wake = V sep 2 V U4 2 Eqn The mixing velocity is again the result of the abrupt flow expansion at the blade passage outlet. It therefore depends on the meridional flow velocity and the geometry of the diffuser blade passage at the outlet. V M,mix = AZV M 4 2πR 4 b 4 Eqn The separation velocity depends on the diffuser divergence angle and the inlet velocity. V sep = V C θ Eqn Going into the diffuser calculation, the code determines the length of the vane based on R 3 and the input area ratio, the throat area, and the incidence angle on the diffuser vane. It then begins the velocity iteration for station 4. After calculating the losses and blockage, a new value for velocity is determined. The process continues until the flow rate at station 4 matches that at station 3, thus conserving mass. The pressure recovery of the diffuser is defined by the portion of the dynamic pressure at station 3 that is recovered as static pressure at station 4. 70

71 Cp = P 4,st P 3,st P 3,t P 3,st Eqn Once the conditions are known at station 4, calculations are mostly complete. During the design portion of RGRC, the static pressure ratio from station 0 to 4 will be compared with the desired pressure ratio, and the impeller diameter (along with the diffuser size) will be adjusted accordingly until the design matches the desired performance. In the off-design portion, efficiencies are calculated and then the next operating condition is run. The total-to-static efficiency is defined as η TS = 4,st 0,t dh aero + I DF + I RC + I Leak Eqn The less frequently used total-to-total efficiency is defined as η TT = 4,t 0,t dh aero + I DF + I RC + I Leak Eqn It is clear that the total-to-static efficiency must be less than the total-to-total efficiency Off-Design Compressor Performance When the code performs a calculation for the performance map, it uses the geometry developed in the design stage and changes the compressor s speed and mass flow rate through a range of values. It performs all the calculations discussed previously; the velocity triangles, losses, and diffuser performance for a range of mass flow rates from 10 % to 300 % of the design flow rate. RGRC performs the calculations for six speeds, selected by the user in the input file. Whether or not the pressure ratio and efficiency of the compressor are displayed in the output for each combination of speed and mass flow rate, is decided by choke and surge. If the compressor has encountered either, the code will not display the output, and if choke has occurred, the code will go on to the next operating speed to be included in the output. In RGRC and RGRCMS, surge is defined as any of the following conditions: 1. A de Haller number (W 1MF /W 2 ) of less than An impeller outlet flow angle with tangent greater than Blockage at the diffuser inlet exceeds 15 % 71

72 Stall could also be experienced by an extreme flow incidence at the diffuser, but experimental data determining where that flow angle lies for CO 2 is not available. In practice, the first two conditions above are sufficiently limiting that severe negative incidence does not occur at the diffuser inlet. Choke occurs when the flow velocity at any point rises above the critical velocity or when losses in the impeller cause the density at the diffuser inlet to fall below the impeller inlet density. This occurs due to excessively high flow rates, since the impeller losses are calculated as pressure losses. The critical velocity database applies to CO 2 and no other fluids have had databases created for them yet. The process of creating a critical velocity database is discussed in Appendix B. RGRC will output the location of choke or surge so that the user can design around the limiting conditions. In RGRCMS the output includes the stage number of the choke or surge also, so the user knows which stage design needs to be improved. 3.4 The Multi-Stage Code RGRCMS The multi-stage code reads in geometric parameters and first stage inlet conditions formed from output of the single stage code. The geometry data required by the multi-stage code is written by a subroutine called MULTISTAGE in RGRC. The multi-stage code assigns the geometrical parameters to vectors with an index identifying the stage number. The code then begins looping through the range of shaft speeds and mass flow rates. Within each combination of shaft speed and mass flow rate, the code proceeds through each stage. After calculating the first stage, the outlet conditions of the first stage are assigned as the inlet conditions of the second stage, with a form loss for the return channel in between. The losses expressed as additional work terms are progressively summed as the code steps through stages. Otherwise, the multi-stage code proceeds almost exactly as does the off-design portion of RGRC. It includes the exact same calculations for impeller and diffuser flows and the losses are calculated with exactly the same subroutines. Stage matching can be difficult and the designer must consider the effects of the return channel on downstream stages. Oftentimes, stall and choke will be a serious issue in downstream stages at mass flow rates that were well within the operating range of the stage when designed independently. This is due to the changing inlet conditions of the second stage as the first stage performance changes. Designing a multi-stage compressor with RGRCMS will inevitably be an iterative process. Multi-stage compressors are usually designed so that each stage has the same static pressure ratio at the design point. The form loss model of the return channel is really not sufficient to describe the effect of the return channel on the flow. The rotation of the fluid will still affect the second stage as the 72

73 velocity changes. This is an aspect of RGRCMS that could use some improvement. The current model does predict the appropriate pressure ratio at the design point and clearly shows that surge and choke are more limiting in the multi-stage design. Also, return channel design may depend a great deal on available space and other factors independent of compressor performance. 3.5 S-CO 2 Compressor Designs Preliminary design estimates are frequently based on specific speed as a way of determining the optimum compressor type, or number of stages. Centrifugal compressors were chosen as the design option for the recompression cycle based on specific speed, and the assumption that the compressors would be synchronized with the electricity grid at 3600 RPM. Testing different approaches to the geometrical design of recompression cycle compressors resulted in the designs detailed in this section. Designs were developed for the compressors needed to operate the 500 MWth PCS described in Chapter The Main Compressor Design The main compressor operates at steady state with the inlet conditions just above the fluid s critical point. The density is very high and therefore the compressor behaves more like a pump. At the design point the main compressor achieves a total-to-static efficiency of 90.4 %. Figures 3.12 and 3.13 show the pressure ratio and efficiency as a function of mass flow rate and operating speed for the main compressor in a 500 MWth representative cycle. At the design point the main compressor work is 32.3 MW. In the reference cycle, the main compressor receives 62 % of the flow, which is a typical value for recompression cycles. Despite the much larger share of the flow, the main compressor work is much less than the recompressing compressor, due to the proximity of the main compressor inlet to the critical point of the fluid. 73

74 Total-to-Static Efficiency Static-to-Static Pressure Ratio % 110% 100% 90% 80% 70% Mass Flow Rate (kg/s) Figure 3.12: The pressure ratio of the main compressor for varying speeds in percentage of the design speed (3600 RPM). The design mass flow rate is kg/s % 110% 100% 90% 80% 70% Mass Flow Rate (kg/s) Figure 3.13: The total-to-static efficiency of the main compressor for varying speeds in percentage of the design speed (3600 RPM). The surge margin in the main compressor is not as large as power producing cycles may require. This is due to the very high density of the fluid necessitating a small blade height at the impeller outlet in order to avoid surge. By reducing the blade height, losses are incurred and the blade height can only be reduced so far in practice. To reduce this problem, a designer could use RGRC to develop a design for a lower mass flow rate, and then just apply that design to the main compressor of the 500 MWth power cycle. 74

75 Static-to-Static Pressure Ratio The Recompressing Compressor Design The recompressing compressor was attempted as single-stage, two-stage, and three-stage designs. The best results were achievable for the two-stage design, in terms of both efficiency and operating range. The single-stage recompressing compressor design achieved undesirable efficiencies (79.8 %) and had a very small surge margin. This is attributable to excessive losses when the pressure ratio is too high for a lower density fluid. The lower density in the recompressing compressor means that a lower stage pressure ratio is needed. At the design point, the two-stage recompressing compressor achieves a total-to-static efficiency of 91.4 %. Figures 3.14 and 3.15 show the pressure ratio and efficiency of the two-stage recompressing compressor at various operating speeds. The inlet conditions of the recompressing compressor are far enough away from the critical point that, although compressing only 38 % of the flow, the recompressing compressor requires 57.0 MW at steady state, about 1.76 times the requirement of the main compressor, despite the fact that the recompressing compressor only receives 38% of the flow % 110% 100% 90% 80% 70% Mass Flow Rate (kg/s) Figure 3.14: The pressure ratio of the recompressing compressor for varying speeds in percentage of the design speed (3600 RPM). The design mass flow rate is kg/s. 75

76 Total-to-Static Efficiency % 110% 100% 90% 80% 70% Mass Flow Rate (kg/s) Figure 3.15: The total-to-static efficiency of the two-stage recompressing compressor for varying speeds in percentage of the design speed (3600 RPM). The design point efficiencies of the recompression cycle designs were incorporated in cycle calculations in Chapter 2. Performance maps similar to these designs have been incorporated in the transient analysis of TSCYCO performed by Trinh [2009]. These compressors display many of the features of ideal gas compressors. They achieve their highest efficiencies at the design point. Pressure recovery in the vaned diffuser is usually achievable up to 0.80 at the design point and efficiencies are rather high overall. As speed increases, the compressor achieves the same peak efficiency, but at a higher mass flow rate. The surge line occurs prior to the flattening of the pressure ratio curves as mass flow rate is decreased. The flattening of the pressure ratio curve can be considered the definition of stall, but the early surge in these performance maps is believed to be indicative of the conservative assumptions in the code Benchmarking RGRC and RGRCMS Benchmarking RGRC is important to validate the code. Few compressors have operated close to the critical point and benchmarking is difficult given the lack of data. A test S-CO 2 compression loop has been operated by Sandia National Laboratory close to the critical point. Some of its parameters are given in Table

77 Pressure Ratio Table 3.3: Selected Sandia Test Compressor Parameters Impeller Diameter 3.7 cm Diffuser Area Ratio 1.90 Blade Thickness 0.40 mm Blade Height at Impeller Outlet 0.62 mm Number of Inlet Blades 6 Number of Outlet Blades 12 Blade Backsweep Angle 40 o Operating Mass Flow Rate 3.53 kg/s Design Speed 75,000 RPM Estimates of the test compressor s geometry have enabled use of RGRCMS to develop a compressor map, but until more experimental data are available, benchmarking is incomplete. The performance maps produced for the design described in Table 3.3 are shown in Figures 3.16 and % 110% 100% 90% 80% 70% 0 Mass Flow Rate (kg/s) Figure 3.16: The pressure ratio of the modeled test compressor for varying speeds in percentage of design speed (75,000 RPM). The design mass flow rate is 3.53 kg/s. 77

78 Total-to-Static Efficiency % 110% 100% 90% 80% 70% Mass Flow Rate (kg/s) Figure 3.17: The total-to-static efficiency of the modeled test compressor for varying speeds in percentage of design speed (75,000 RPM). The design mass flow rate is 3.53 kg/s. The Sandia test compressor, operating at 75,000 RPM and 3.53 kg/s with inlet conditions of 7.69 MPa and 305 K achieved a pressure ratio of 1.8 and a total-to-static efficiency of 66.0 % [Wright et al., 2008]. The steady-state operating speed is really a lower value than 75,000 RPM. It is actually closer to 45,000 RPM. The performance maps produced by RGRCMS are reasonably accurate considering that dimensions were determined by looking at a photograph of the test compressor. Continued operation of this test compressor and input of more precise geometry will yield more data and eventually RGRC can be effectively benchmarked. Currently, the exact dimensions of the impeller are not available for release, nor are tabulated data. 3.6 Chapter Summary A mean-line compressor code was developed using the NIST fluid property polynomials as a means of sizing and estimating performance for S-CO 2 compressors to be used in the recompression cycle. This code produces results for single and multi-stage compressors, estimating losses based on experimental correlations. It is a first step in designing actual compressors. The geometry of the compressor impeller can be manipulated by the user in a single input file and the code performs sizing of the impeller and related diffuser to achieve the desired pressure ratio at the design point. Off-design performance estimation is automatic for the resulting design. RGRC produces a performance map for the stage in a single output file with the important geometrical parameters. RGRC also produces an output that can be used with other stage outputs in the multi-stage code, RGRCMS. 78

79 The codes incorporate fluid property polynomials produced by Yifang Gong which speed up calculations for CO 2. These are suitable for the range of applications that recompression cycles require, but can be backed up with NIST fluid property subroutines as well. This compressor code has been used to estimate the performance of Sandia s test compressor, as a start on benchmarking the code. Results of the benchmarking attempt show that the codes operate without any problems at high relative velocities and that the codes are consistent with expectations. The much smaller Sandia compressor has a similar specific speed to the larger compressor designs and its performance was shown to be similar as well. S-CO 2 recompression cycle compressors achieve total-to-static efficiencies greater than 90 % at the design point and they display none of the anomalous features that plagued CCODS in their compressor maps. Multi-stage designs are now possible, up to three stages, and the use of multiple stages becomes necessary for the recompressing compressor of the 500 MWth cycle. 79

80 3.7 Nomenclature for Chapter 3 a speed of sound (m/s) A Flow area (m 2 ) b blade height (m) B D D hyd Blockage (dimensionless) Impeller diameter (m) hydraulic diameter of a passage (m) g acceleration due to gravity (m/s 2 ) h enthalpy (J/kg) H pressure head (m) I Loss (J/kgK) L b blade length (m) Ns Specific Speed (dimensionless) P Pressure (kpa) R radius (m) Re Reynolds number s entropy (J/kgK) t thickness (m) T Temperature ( o C) U Blade velocity (m/s) V Absolute flow velocity (m/s) V cr W Z Greek Letters (for Compressors) α β δ η μ ω Ω critical velocity (m/s) Relative flow velocity (m/s) Number of Blades Absolute flow angle Relative flow angle Boundary layer thickness (m) Efficiency Viscosity (Pas) fractional pressure drop Rotational speed (rad/s) φ Flow Coefficient ρ Density (kg/m 3 ) θ C χ Diffuser divergence angle Blade angle (rad) 80

81 Subscripts (for Compressors) 1 Inducer inlet 2 Impeller outlet 3 Diffuser Inlet 4 Diffuser outlet b full length blade BL Blade loading CL Tip Clearance DF Disk Friction e roughness eff effective eq equivalent EXP Expansion HS Hub-to-Shroud INC Incidence LE Leading Edge Leak leakage losses M meridional MIX Mixing MF At the RMS radius RC Recirculation rel relative rms root mean square SEP Separation SF Skin Friction split splitter blade st static SS Static-to-Static TE Trailing Edge th throat TS Total-to-Static TT Total-to-Total t, tot total U tangential vane diffuser vane wake diffuser wake flow 81

82 4 Balance of Plant Options 4.1 Introduction Necessary Tools for Analysis SFRs are among the reactor concepts included in the Generation IV Roadmap [GIF, 2002]. They have the potential to be built as, burners, break-even or breeder cores. Their relatively high core outlet temperature means that significant efficiency gains could be achieved over current LWR technology. The choice of balance of plant, heat exchanger type and dimensions, and intermediate loop will affect the overall efficiency of the SFR a great deal. The ABR-1000 design claims a Rankine cycle efficiency of ~38 %, but the cycle efficiency alone doesn t tell the whole story. The pumping power of primary and intermediate pumps is important, and the net cycle efficiency can be improved or degraded by design changes from the reference case. As shown in Figure 2.4, the cycle efficiency is strongly dependent on the turbine inlet temperature and the choice of cycle. In order to understand where efficiency improvements could be made, many design configurations needed to be investigated. A principal such configuration is the use of Printed Circuit Heat Exchangers (PCHEs) for the secondary intermediate heat exchanger (S-IHX) or primary intermediate heat exchanger (P-IHX). PCHEs are compact and rugged. They could replace shell-and-tube designs in the SFR plant if sodium plugging is shown to be avoidable in small channels. The S-CO 2 cycle will make higher plant efficiencies a possibility for higher turbine inlet temperatures. Additionally, elimination of the intermediate loop will reduce the temperature difference between the primary fluid and the PCS working fluid, thus increasing turbine inlet temperature. All these changes need to be evaluated for their effect on efficiency. Tools already available at MIT for this analysis included CYCLES III for the S-CO 2 PCS and a number of PCHE codes written by Pavel Hejzlar [Hejzlar et al., 2007]. There was no available model at MIT for shell-and-tube heat exchangers, nor do the PCHE codes cover all of the cases of interest to this study. These existing tools also do not take into account efficiency losses due to heat conduction from intermediate piping or pumping power losses in either the primary or intermediate loops. Heat losses in intermediate piping are negligible and do not produce any real change in the plant efficiency. Pumping power for the entire plant can reach almost 1 % of the core thermal power, so it is important for efficiency considerations. 82

83 The most important factors in the efficiency of SFRs are therefore: 1. Core outlet temperature 2. Heat Exchanger Design 3. PCS efficiency 4. Total System Pump work These four items will be evaluated in Chapter 5, but in order to do so, some tools need to be developed. These include heat exchanger models for both the P-IHX and the S-IHX, models of the achievable efficiencies for Rankine, supercritical steam, and S-CO 2 cycles, and a discussion of the likely range of achievable core outlet temperatures. With these important considerations in mind, the task of expanding the modeling capability was undertaken. The major goals were to: 1. Develop a shell-and-tube code to model sodium-sodium or sodium-co 2 heat exchangers 2. Develop a straight tube shell-and-tube steam generator model 3. Develop a PCHE model for sodium-sodium heat exchangers 4. Develop a PCHE model for a sodium-water steam generator 5. Model the intermediate heat exchanger pressure drops to determine pumping power 6. Show that heat lost through insulated intermediate loop piping is negligible First, simple calculations of pumping power and heat lost through intermediate piping are performed. Then, descriptions of the more involved calculations are included in later sections. Sodium properties are calculated using correlations from a study of sodium at Argonne National Laboratory [Fink and Leibowitz, 1995] Heat Losses in Intermediate Piping and Pumping Power of an SFR The heat lost in the intermediate loop piping is negligible in an SFR. This can be shown by performing some simple calculations based on convective heat transfer from the sodium flow to the air outside. The temperature changes in the sodium flow are negligible in the intermediate loop, allowing the system to be modeled as though temperatures are identical at positions 2 and 3 and at positions 1 and 4 shown in Figure 4.1. This can be shown by assuming a constant linear heat rate in the sodium piping from 2 to 3. If the ambient air is at a temperature of around 300 K and the sodium is in the range of typical SFR temperatures, then the temperature difference from the sodium to the air will be ~450 o C. The linear heat rate will be given by 83

84 q = 1 πd 1 Na + ln d 2 d 1 2πk pipe + ln d 3 d 2 2πk ins + 1 πd 3 air 1 (450 o C) Eqn. 4-1 where d 1, d 2, and d 3 are the pipe inside diameter, pipe outside diameter, and the insulation outside diameter, respectively. The thermal resistance of the insulation is the dominant term in Eqn. 4-1, contributing about 91 % of the resistance even for the thinnest insulation of just 1 cm. Using the Clinch River Breeder Reactor (CRBR) as an example shows that the temperature changes in the intermediate loop are negligible. CRBR was chosen as an example because it is matches the ABR-1000 closely in intermediate loop mass flow rate and temperatures. It also has the highest intermediate loop pumping power of any SFR, so it is a conservative example. The temperature drop in the intermediate loop from points 2 to 3 is determined by calculating the heat transfer to the atmosphere. Representative values used in Eqn. 4-1 are given in Table 4.1. From Core 2 3 To PCS P-IHX S-IHX To Core 1 4 From PCS Figure 4.1: Schematic of the intermediate loop. The P-IHX could be incorporated in a loop design (as pictured) or submerged within a pool of primary coolant. 84

85 Table 4.1: Representative Values used in Eqn. 4-1 Pipe inside diameter d m Pipe outside diameter d m Insulation outside diameter d 3 Variable Mass flow rate m 1256 kg/s Conductivity of the pipe k pipe 21.0 W/mK Conductivity of Insulation k ins 0.04 W/mK Temp. of Sodium T 510 o C Conductivity of Sodium k Na W/Mk Heat Capacity of Sodium Cp J/kgK Density of Sodium ρ kg/m 3 Viscocity of Sodium μ E-4 Pas Heat transfer coeff. of air h air 40 W/m 2 K [Mills, 1995] The value of the heat transfer coefficient for the ambient air is conservatively chosen to be high. The results show that the insulation provides the most significant thermal resistance, and that even relatively high heat transfer coefficients on the air side do not result in significant heat losses in the intermediate piping. The sodium Nusselt number was calculated using a correlation by Notter and Sleicher [Todreas and Kazimi, 1993] Nu = Re 0.85 Pr 0.93 Eqn. 4-2 Based on an assumed intermediate pipe length of 24 m from point 2 to 3, the coolant temperature difference between points 2 and 3 can be plotted as a function of insulation thickness, as shown in Figure 4.2 for a 250 MW loop. Even for very thin insulation, the temperature difference is very small. Figure 4.3 shows the heat lost to the environment by this example loop, also as a function of insulation thickness. Both the hot and cold legs of the intermediate loop will experience similar losses because the fluid properties of sodium do not change much with temperature. The cold leg will lose about 33 % less heat than the hot leg because the temperature difference between the cold leg and ambient air is about 155 o C less than that of the hot leg. 85

86 Heat Lost (kw) Temperature Drop ( o C) Thickness of Insulation (m) Figure 4.2: The temperature drop through the 24 m long intermediate pipe, as a function of insulation thickness The heat lost by the intermediate coolant, corresponding to this temperature drop, is shown in Figure 4.3. Despite the high heat capacity of sodium, the temperature drop is so small that very little heat is lost through the intermediate piping walls Thickness of Insulation (m) Figure 4.3: Heat Lost in through the 24 m long intermediate pipe, as a function of insulation thickness 86

87 The thermal resistance of the insulation is so high that changes in the insulation s thermal conductivity result in almost perfectly linear responses in heat lost. Thus, if the conductivity of the insulation is underestimated by a factor of three, then the corresponding results in Figures 4.2 and 4.3 are just a multiple of three higher, which is still very little heat lost. In the intermediate loop sodium pump, the temperature rise is also very small. The pumping power for an incompressible fluid is given by W pump = ΔPm ρ Eqn. 4-3 The CRBR, whose intermediate pipes served as a model for the calculation above, has an intermediate pump head of 0.86 MPa. The CRBR is a conservative test case because it has one of the highest pumping powers for SFRs, as shown in Table 4.2, and the CRBR matches the ABR-1000 closely in intermediate loop mass flow rate and temperature [IAEA, 2006], as shown in Table 4.3. Table 4.2 Intermediate Loop Pumping Power Requirements for SFRs Reactor Intermediate Pump Head (MPa) CRBR (USA) 0.86 Super-Phenix 1 (France) 0.25 ALMR (USA) 0.34 BN-1600 (Russian Federation) JSFR-1500 (Japan) Table 4.3 Characteristics of CRBR and ABR-1000 Intermediate Loops CRBR ABR-1000 Hot Temperature ( o C) Cold Temperature ( o C) Mass Flow Rate (kg/s) Intermediate Loop Power (MWth) Number of Loops 3 4 With the head requirement of 0.86 MPa, the pump work comes out to 1.30 MW for the intermediate pump. The sodium temperature rise through the pump is given by 87

88 T = W pump 1 1 η 1 m c p Eqn. 4-4 for a fluid with constant specific heat capacity, where η is the polytropic efficiency of the pump, c p is the specific heat capacity of the fluid, and the pump work is calculated as before. Constant specific heat capacity is a good assumption for liquid sodium within the intermediate loop. If the pump is 75 % efficient, this results in a temperature rise of 0.27 o C, which is negligible. Basically, the intermediate piping can be ignored for efficiency studies, with the exception of the pump work s effect on overall plant efficiency. The pumping power of the intermediate loop has already been shown to have very little effect on the temperature of the fluid. Pumping power in the intermediate loop will depend a great deal upon the size and type of heat exchangers used. In the primary fluid, pumping power is greater due to pressure drops in the core and in primary piping (for a loop design). In the ABR-1000 reference case each of the primary pumps in ABR-1000 requires 1.15 MW of power if perfectly efficient, based on a pressure head of 0.76 MPa and a flow rate of 90.9 m 3 /min. To overcome the friction pressure drops within intermediate piping and heat exchangers, the pump work of each intermediate loop pump is about 340 kw if perfectly efficient. Because centrifugal sodium pumps can be expected to have efficiencies between % [Grandy and Seidensticker, 2007], the total pumping power required for the ABR-1000 plant is from about 7.0 MW to 8.5 MW for a 1000 MWth plant, including both primary and intermediate sodium pumps. Therefore, reducing pressure drops and quantifying pump work are certainly important from a plant efficiency standpoint. 4.2 Alternate Fluids in the Intermediate Loop Sodium has been used as the working fluid in the intermediate loop in SFRs due to its extremely good thermodynamic properties. Using other fluids has been considered as an option in previous research. Here, these results are reported so the reader is familiar with work that has already been completed. Elemental liquids, organics, inorganic salts, gases, and gas-solid suspensions were investigated in a study of thirty different heat transfer media by Cooper and Lee [1975]. They were compared on the basis of required heat transfer area, pumping power, melting points, and chemical reactivity. Their conclusions are summarized as follows: Liquid Metals: Heat transfer areas and pumping powers for liquid metals are all comparable to sodium, however, many react nearly as strongly with water. Work has been done on leadbismuth eutectic reactors in numerous studies. These have been interesting since the solution of some practical problems in a comprehensive Russian development program [Hejzlar et al., 88

89 2000], but lead-bismuth eutectic fails to perform better than sodium due to excessive pumping power. On the whole, no liquid metals perform better than sodium from a heat transfer comparison, though some are comparable. The lead-bismuth eutectic is attractive for its low reaction rate with water. Molten Salts: All of the salts studied require a higher heat transfer area than sodium. Some are explosively reactive with sodium, and excessively high melting point is a problem for others. Organics: Organics thermally decompose at temperatures above 427 o C, which is well below the temperatures of interest to SFRs. Simple gases: Gases don t perform as well as a heat transfer medium, and their pumping power is often orders of magnitude greater than that of sodium. Gas-solid suspensions: Gas-solid suspensions require times the heat transfer area of sodium, making them impractical. As a heat transfer medium sodium is the best available and it enjoys lower pumping powers and a greater useful temperature range than any other option. Consequently, for the intermediate loop sodium is still the best option. The lead-bismuth eutectic coolant is also appealing due to its inertness in terms of reactions with water. Bismuth does not react with water and lead releases only 1.5 % of the heat that sodium does in a reaction with water, per unit mass of reactant. The pumping power requirements for lead and bismuth are factors of 4.18 and 3.67 higher, respectively, than that of sodium. The pumping power of the intermediate loop is low compared to that of the primary loop, but substituting a lead-bismuth eutectic for sodium would make the intermediate pumping power comparable to the primary pumping power. 4.3 Eliminating the Intermediate Loop The intermediate loop in operating SFRs is a safety measure to reduce the radiological consequences of a sodium-water or sodium-air interaction. By including the intermediate loop, primary sodium is isolated and the danger of a radiation release is mitigated in accidents involving leaks in the P-IHX. Eliminating the intermediate loop will have substantial efficiency gains, however, and the safety consequences may not be severe enough to warrant the requirement of an intermediate loop. The effects of eliminating the intermediate loop on core damage frequency (CDF) or large early release frequency (LERF) are not examined here. Instead, the calculations performed were aimed only at determining the efficiency benefit for the system if the intermediate loop were eliminated. Probabilistic Risk Assessments (PRA) of the 89

90 effect on plant damage states is important to determining whether a design configuration is acceptable. Efficiency improvements may be outweighed by increased risk. Eliminating the intermediate loop is a much more feasible option in loop designs for SFRs. One reason is the required heat transfer area of intermediate heat exchangers and the core dimensions of SFRs. SFRs are generally short, squat cores due to the requirement to avoid designing a core with too high of a coolant void worth [Wigeland et al., 1994]. For that reason, the vertical temperature change from core inlet to core outlet in a pool reactor will only span about 5.0 m, the height of the core. Large heat transfer areas would require tall heat exchangers unless the reactor vessel can be substantially enlarged radially. Either way, inclusion of a steam generator inside a pool reactor vessel would require substantial enlargement of the vessel in height or diameter or both. Also, the safety consequences of eliminating the intermediate loop in a pool design are such that the design is not likely to be licensable. Loop designs allow for the use of a taller P-IHX and do not include the hazard of a large secondary coolant blowdown within the reactor vessel. Further discussion of this option is included in Chapter 5, as the different configuration options are examined. 4.4 PCHE versus Shell-and-Tube Heat Exchangers In order to compare design options with different combinations of heat exchanger designs, a method for modeling heat exchanger performance was necessary. MIT s in-house PCHE code models printed circuit heat exchangers. It was written by Pavel Hejzlar [Hejzlar et al., 2007]. A flexible model of shell-and-tube heat exchangers was needed to provide a first estimate of the size of these heat exchangers. A Fortran code named SoSaT (Sodium Shell and Tube) was written to accomplish this, so that different types of shell-and-tube heat exchangers could be analyzed in a short period of time. When this project was undertaken, however, the PCHE codes had the following capabilities: Sodium to gas hybrid heat exchangers Sodium to gas direct PCHE Gas to gas direct PCHE Water to Water Two Phase PCHE [Shirvan, 2009] Additions were made to the list of capabilities such that these codes can now model: Sodium to Sodium direct PCHE Sodium to Water Two Phase Hybrid PCHE 90

91 In optimizing the recompression cycle, CYCLES III treats the IHX very simply, requiring a pressure drop, power rating, and turbine inlet temperature as the only inputs related to the IHX. Mass flow rate is scaled with the power as 3000 kg/s m = Q Eqn MW where Q is the thermal power input in the IHX. This scaling of mass flow rate with power has been a feature of the CYCLES code since its original version. The only PCHE type that needs to be modeled within CYCLES III is the gas-to-gas recuperator because CYCLES III only requires pressure drop, power, and temperature for the IHX. Therefore, the existing codes proved sufficient for optimizing the S-CO 2 balance of plant. In order to model the heat exchangers of the entire system, the PCHE modeling capabilities required expansion and a shell-and-tube code needed to be written The Shell-and-Tube Code SoSaT In order to size shell-and-tube heat exchangers, a Fortran code called SoSaT (Sodium Shell and Tube) was written. The code has the capability to size sodium-sodium, sodium-co 2, or sodium-water heat exchangers. The code can perform calculations for single phase, boiling, or supercritical water. For sodium-sodium and sodium-co 2 heat exchangers, the method of the number of transfer units (NTU) is used. NTU is an expression of the heat exchanger effectiveness relative to the overall heat transfer coefficient and fluid heat capacities [Shah, 2003]. The relationships between heat transfer coefficient, NTU and effectiveness are summarized as follows: UA 1 = 1 L 1 + log d o,o/d i,i 1 + Eqn. 4-6 πd i,i tube 2πk tube πd o,o Na where UA is the product of the overall heat transfer coefficient and the heat transfer area. The number of transfer units is based on the overall heat transfer coefficient and the mass flow rates and heat capacities of the two fluids. NTU = UA/MIN(C1, C2) Eqn. 4-7 where C1 and C2 are the products of mass flow rate and heat capacity for each fluid. The effectiveness is related to NTU by 91

92 where C* is given by ε = exp NTU 1 C 1 exp NTU 1 C C Eqn. 4-8 C = MIN(C1, C2)/MAX(C1, C2) Eqn. 4-9 The sodium heat transfer coefficient, in un-baffled counter flow along a tube bank, is given by the Westinghouse correlation [Todreas and Kazimi, 1993] Nu Na,cflow = P/d RePr/ P/d 5.0 Eqn Na = Nuk Na D yd Eqn where the Reynolds number is calculated as the average value from the sodium inlet to the outlet, based on hydraulic diameter. When baffles are used on the shell side, the Bell-Delaware method is used to determine the heat transfer coefficient [Shah, 2003]. Baffles cause the flow to be more mixed and to follow an almost cross-flow pattern through the tube banks. This enhances the shell side heat transfer coefficient. The Bell-Delaware method correlates correction factors to a cross-flow heat transfer coefficient based on the baffle geometry. The cross-flow Nusselt number for sodium is given by the Kalish-Dwyer correlation [Foust, 1976]. Nu Na,xflow = φ 1 d 1 d P Pe0.653 Eqn xflow = Nu Na,xflow k Na D yd Eqn where φ 1 is an empirical constant which is determined from tabulated values by Hsu [1964]. The resulting heat transfer coefficient is given by s = xflow J c J r J b J s J l Eqn where the correction factors, J, are given according to Table

93 Table 4.4: Correction factors for the cross-flow Nusselt number from the Bell-Delaware Method Correction For The cut of the baffles Leakage around the baffles Correction Factor J Notes Definitions J c = F c Eqn J l = r s r s exp 2.2r lm Eqn F c = 1 θ ctl + sinθ ctl π Eqn θ ctl = 2cos 1 D s 2l c D ctl Eqn r s = A o,sb A o,sb + A o,tb Eqn r lm = A o,sb + A o,tb A o,cr Eqn D s = shell diameter l c = dist. baffle edge to shell D ctl = tube array diam. - tube diam. A o,sb = shell-to-baffle leakage area A o,tb = tube-to-baffle leakage area A o,cr = cross flow area Bundle bypass flow J b = 1 for N ss + 1/2 exp Cr b 1 (2N ss + ) 1/3 for N ss + 1/2 Eqn N ss + = N ss N r,cc Eqn r b = A o,bp A o,cr Eqn N ss = the number of sealing strips or obstructions to bypass flow Temperature Gradient Buildup J r = 10 N r,cc 1 for Re for Re 20 Eqn C = 1.35 for Re for Re > 100 Eqn N r,cc = number of tube rows in cross flow zone Baffle Spacing at inlet and outlet J s = N b 1 + (L i + ) (1 n) + (L o + ) (1 n) N b 1 + L i + + L o + Eqn n = 0.6 turbulent flow Eqn laminar flow N b = number of baffles L i + = entrance baffle spacing L o + = outlet baffle spacing 93

94 For a P-IHX, with sodium on the tube side, the heat transfer coefficient is given by Nu Na,tube = Re 0.85 Pr 0.93 Eqn for upward flow of sodium in tubes [Mills, 1995]. For S-CO 2 flow on the tube side, Kim et al. [2008] have modified the Jackson and Fewster correlation for supercritical pressures in smooth tubes. Given that the operating pressure of S-IHXs will be much higher than the critical pressure of MPa, the correlation can be used to produce a Nusselt number that applies to the entire heat exchanger once the Reynolds and Prandtl numbers are obtained from average properties at the inlet and outlet. Kim et al. [2008] determine the S-CO 2 Nusselt number to be Nu = Re Pr ρ wall ρ bulk Eqn For enhanced tubes, the Ravigurarajan and Bergles correlation is used to determine the heat transfer coefficient [Ravigurarajan and Bergles, 1996]. The enhancements consist of spiral ribs on the interior of the tubes. Pressure drops are increased, but the heat transfer can be vastly improved, saving a great deal in terms of the size of the heat exchanger. The Ravigurarajan and Bergles correlations for heat transfer and pressure drop are excluded here due to their length, but they can be found in Appendix D. In all designs discussed hence, enhanced tubes are assumed to be used for CO 2 only. The experiments used to develop enhanced tube correlations were conducted with air and single-phase water, so other fluids are assumed to be outside the range of validity of their correlations. With the average heat transfer coefficients determined for the two fluids, the overall heat transfer coefficient can be calculated. For sodium-sodium heat exchangers, single-wall tubes are appropriate, but to ensure a leak detection capability and increase the robustness of S-IHXs, double-walled tubes are assumed to be required in a sodium-co 2 or a sodium-water heat exchanger. The work of Kubo et al. [1997] produced results for the effective thermal conductivity of a 9Cr-1Mo double-walled steam generator tube. Using this data, and a thermal conductivity of 9Cr-1Mo steel of 27.9 W/mK [Williams et al., 1984] the value of the effective gap conductivity was determined to be mw/mk. This value for effective helium gap conductivity has been used in SoSaT so that the user may define a double-walled tube of any wall thickness and any material. It should be noted that the experiments of Kubo et al. were conducted for a beginning of life (BOL) gap thicknesses of 3 μm and the end of life (EOL) gap thickness was measured to be ~7 μm. Comparison of the calculated value of gap conductivity with the conductivity of helium at 400 o C and 0.90 MPa, the 94

95 condition of the experiment performed by Kubo et al., reveals that the gap is behaving almost exactly as a stagnant gas thermal resistance. REFPROP determines the conductivity to be mw/mk. SoSaT will calculate the ASME required thickness of tubes based on the material chosen, the operating temperature, and the internal pressure based on Eqn The allowable stress intensity for each material is interpolated from ASME Code tabulated values assuming a temperature equal to the hot side inlet temperature [ASME, 2007]. These calculations are contained in the subroutines MATPROP and GEOMETRY. For single phase fluids, the heat transfer coefficients, tube conductivity and dimensions are then used in the subroutine EFFECTIVE to determine the overall heat transfer coefficient and NTU. Then the effectiveness is calculated and outlet temperatures are based on the effectiveness. The process is continued by iterating the outlet temperatures of each fluid until convergence. The NTU method is not used in steam generators because the heat transfer coefficients and fluid properties vary widely through different boiling regimes. Therefore, SoSaT is really two codes which share common inputs and outputs. The calculation method is totally different for boiling water than it is when both fluids are single phase. Modern steam cycles employ ever-increasing system pressures as a means of increasing cycle efficiency. Substantial efficiency gains can be achieved by raising steam pressures, even above the critical pressure of MPa [MIT, 2007]. Therefore, it is assumed that Generation IV reactors operating on a steam cycle will have system pressures considerably higher than those of current LWR steam cycles. Modeling the heat transfer within high pressure steam generators requires the use of appropriate experimental correlations for the heat transfer coefficients within different boiling regimes. The boiling process, as modeled by SoSaT is summarized in Figure

96 Figure 4.4: The division of the tube length according to heat transfer regime in SoSaT. The shell-and-tube steam generator model assumes that sodium will flow in a uniform manner downward through a cylindrical shell. There is no option for baffles in the current steam generator model. Upward flow of water is contained in a hexagonally pitched bank of smooth surfaced tubes. The tubes are assumed to be double wall tubes and can be constructed of several materials. These are 9Cr-1Mo steel, 304 SS, and 316 SS. The code begins by calculating what the sodium outlet temperature must be, assuming that all of the designated power is transferred as heat to the water. Based on the sodium inlet conditions, the heat transferred is given by Q = m Na c p avg T Eqn By assuming that the specific heat capacity of sodium does not change appreciably with temperature, the outlet temperature is calculated from Eqn. 4-30, using the user s input of total heat to be transferred. The specific heat of sodium at each temperature is calculated based on known fluid properties from an Argonne National Laboratory study [Fink and Leibowitz, 1995] 96

97 and the process is iterated until the sodium outlet temperature converges. This outlet temperature is necessary for determining the fluid properties (and then the heat transfer coefficient) of sodium at the bottom of the shell, where the first node of the heat transfer calculation lies. The calculation will proceed upward in nodes of 1 cm length. The critical heat flux is determined for each node from interpolation of Groeneveld s 2006 CHF Lookup table [Groeneveld, 2007], which requires tube diameter, mass flow rate, pressure, and quality as inputs. This calculation occurs at each node because many of these parameters will change at each node. The sodium heat transfer coefficient is calculated based on properties obtained from the outlet temperature and the Westinghouse correlation for liquid-metal, counterflow heat transfer in a tube bundle. Nu = P/d RePr/ P/d 5.0 Eqn Based on conditions on the tube side, an appropriate heat transfer correlation will be chosen. When the water is still subcooled, the Dittus-Boelter correlation is used. The code identifies subcooled water by the wall temperature and the bulk fluid temperature. H2O = 0.023Re 0.8 Pr 0.4 k/d Eqn and friction factors are given by the Blasius or McAdams correlation, according to the Reynolds number. f = 0.316Re 0.25, Blasius correlaion: Re < 30, Re 0.20, McAdams correlation: Re 30,000 Eqn The code assumes that, until saturation, all heat transfer to the water manifests as a temperature rise. This is valid on a bulk fluid basis, and since the total length of pipe is more interesting than the details of the flow, the assumption is used in SoSaT. Therefore, the temperature increase of the subcooled fluid is given by T bulk = dq Eqn m H2Oc p where dq represents the heat transferred in the node. The fluid reaches subcooled boiling when the wall temperature reaches a minimum value above the saturation temperature. This point is termed the onset of nucleate boiling. The temperature above which the wall must rise is given by 97

98 T wall = T sat + 8σq ONB T sat h fg k f ρ g 0.5 Eqn which was developed by Davis and Anderson [1966]. Once the wall temperature reaches this value, the flow enters the subcooled boiling regime. The heat transfer coefficient of the subcooled boiling region is given by sub = TP T wall T sat T wall T f + lo Eqn where h lo indicates the liquid only heat transfer coefficient given by the Dittus-Boelter correlation and h TP is the two-phase nucleate boiling heat transfer coefficient given by Kandlikar [1990]. TP lo = C 1 Co C 2(25Fr lo ) C 5 + C 3 Bo C 4F fl Eqn Once the bulk temperature has reached saturation, the Kandlikar correlation predicts the rise in quality for each node according to the heat of vaporization. This regime is saturated nucleate boiling. Critical heat flux is still tested for in each node and once it is surpassed, the code switches to the Bishop correlation for post-dryout heat transfer [Groeneveld, 1975]. The heat transfer coefficient after dryout is given by Nu = 0.033Re w 0.80 Pr w 1.25 x + ρ g ρ l 1 x ρ g ρ l Eqn which is valid up to quality of 1.0 and pressures up to 21.5 MPa. Once the equilibrium quality reaches 1.0, the Gnielinski correlation for vapor heat transfer coefficient is used. It gives the Nusselt number as Nu = f 2 Re g 1000 Pr g Pr g f 2 Eqn f = Re g Eqn The calculation concludes once the prescribed power has been transferred to the fluid. The test for heat transferred is the condition for continuation of the loop, so even if the flow never enters 98

99 the superheated vapor regime, the calculations will stop once the total desired power is transferred. For supercritical water, modeling the heat transfer is much easier since the water does not undergo a distinct phase change. In the case of supercritical pressures, the water side heat transfer coefficient is determined by the correlation of Cho, Chou, and Cox [Herron, 2002]. Nu s H2O = Gd μ bulk wall bulk T wal l T bulk μ wall k ρ wall ρ bulk Eqn For supercritical pressures, the Cho, Chou, and Cox correlation will be acceptable, assuming that pressure drops never cause the fluid to fall below the saturation dome. The critical pressure for water is MPa. The conditions tested at each node determine which boiling regime the water has entered, and therefore which correlations to use for the heat transfer coefficient and pressure drop. Table 4.5 summarizes the criteria for each boiling regime based on bulk temperature, wall temperature and equilibrium quality, x. Heat Transfer Regime Table 4.5: Conditions for each boiling regime in SoSaT Heat Transfer Correlation References Conditions* Subcooled Liquid Dittus-Boelter [Todreas and Kazimi, 1993] T bulk <T sat, T wall <T sat + ΔT Subcooled Boiling Kandlikar [Kandlikar, 1990] T bulk <T sat,t wall >T sat +ΔT Saturated Nucleate Boiling Kandlikar [Kandlikar, 1990] x>0.0,x<1.0, q,q crit Post CHF heat transfer Bishop [Groeneveld, 1975] x<1.0, q >q crit Vapor Gnielinski [Rohsenow et al., 1998] x>1.0 * ΔT is represented by the second term in Eqn To aid in the operation of SoSaT, the code outputs the difference between the bulk temperature and saturation temperature, along with the boiling regime to the screen every 10 cm in the upward flow calculation. That way, the user can see if the prescribed geometry has resulted in a pinch-point or if an excessively high flow rate has resulted in poor steam conditions without ever opening the output file. 99

100 4.4.2 Expanding the Capabilities of the PCHE Codes The PCHE codes needed to have a hybrid steam generator model and a sodium-tosodium model added. Creating a sodium-to-sodium PCHE model was very simple. The existing PCHE code with no helium plate was altered by taking the primary sodium properties and applying them to the secondary side as well. The task was almost trivial. Creating a steam generator model for the PCHE was more difficult. The original hybrid code was altered by including a new heat transfer subroutine and CHF calculations. The heat transfer subroutine was modified from Shirvan [2009] to include the same high pressure correlations as SoSaT. One challenge with the PCHE code was dealing with convergence. The code operates by calculating the heat transfer coefficient of each fluid at its average temperature. This heat transfer coefficient is then used to make a rough judgment of the size of the heat exchanger, and therefore the size of each node. The wide variation in boiling water heat transfer coefficient meant that the initial guess was far from correct and the code s node length was too long. The result was that the code stepped beyond the desired power of the heat exchanger and crashed. Resolving this error by stopping calculations once the desired power is reached allowed the code to run smoothly. 4.5 Benchmarking Heat Exchanger Codes There are not enough data available to benchmark PCHE code results, but the shell-andtube design has been used in many reactor designs. For S-CO 2 heat exchangers, the Flexible Conversion ratio Reactor (FCR) IHX was used as a case for comparison. The FCR is a leadcooled reactor with S-CO 2 power conversion system. It uses kidney shaped IHXs, so for comparison, the geometry of the tube array and the total number of tubes was retained from the FCR analysis. The comparison between the FCR IHX and that produced by SoSaT is included in Table 4.6. Also included are benchmark designs for a shell-and-tube P-IHX from the ABR design, and a shell-and-tube steam generator from the JSFR design. 100

101 Table 4.6: Benchmarking of SoSaT code** Reference Design SoSaT Results Reactor Design FCR IHX Number of Tubes S-CO 2 heat transfer coeff. (W/m 2 K) Lead Heat transfer coeff. (W/m 2 K) Tube length (m) Reactor Design ABR-1000 P-IHX Number of Tubes Primary heat transfer coeff. (W/m 2 K) N/A Secondary heat transfer coeff. (W/m 2 K) N/A Tube length (m) Reactor Design JSFR Steam Generator Number of Tubes Sodium heat transfer coeff. (W/m 2 K) N/A Water heat transfer coeff. (W/m 2 K) N/A variable Heat transfer area (m 2 ) * *Including a 20% margin on the heat transfer area, as is common practice in steam generator design would yield a value closer to the reference JSFR design. **[Grandy and Seidensticker, 2007], [IAEA, 2006], [Todreas and Hejzlar, 2008] For the benchmark designs, tube dimensions and pitch were identical to the reference design. The number of tubes for each design is a result of the shell geometry, so it does not match the reference designs perfectly, but it comes close for each design. Heat transfer coefficients are averages that where given in the FCR reports or calculated in SoSaT and are not available for the ABR-1000 or JSFR reference designs. The FCR IHX includes enhanced tubes which were replicated in the SoSaT design. The improvements over smooth tubes are similar for the FCR design and the SoSaT model of the same heat exchanger. The results of SoSaT are in very good agreement with reference designs. 4.6 S-CO 2, Traditional Rankine, or Supercritical Steam PCS Commercial power SFRs have used the traditional Rankine cycle, though at temperatures and pressures higher than those of LWRs. Supercritical steam cycles have been operated in some coal fired power plants [MIT, 2007] with pressures up to 24.3 MPa and temperatures of 565 o C. Achievable generating efficiency of these plants is about 38 %. Target steam conditions 101

102 Cycle Efficiency (%) are up to 38.5 MPa and o C. Supercritical CO 2 cycles are promising for any high temperature application. All of these technologies could be options for the SFRs of the future, but they will inevitably produce different cycle efficiencies. The trend in conventional power technology is to use steam cycles of ever-increasing pressures because cycle efficiency improves with increased pressure, as shown in Figure 4.6. These data were developed using a standard commercial steam cycle model with a high and a low pressure turbine and four reheat stages. The feedwater temperature is maintained constant at 216 o C, as per the ABR-1000 reference case. Cooling water is at 20 o C. The data were obtained using STEAM PRO 16, steam cycle modeling software from Thermoflow, Inc. [Thermoflow, 2008] MPa 15.5 MPa 16.5 MPa Turbine Inlet Temperature ( o C) Figure 4.6: Rankine Cycle efficiency as a function of temperature and pressure The S-CO 2 cycle has already been discussed in detail in Chapter 2. It can achieve very high efficiencies and is compact. The S-CO 2 recompression cycle will be one of the options considered in Chapter 5. The supercritical water cycle shows promise for the future. Corrosion is an issue in a supercritical water environment, but efficiency gains can be realized. A good model of the supercritical water cycle was not available in this research, but gains over conventional Rankine cycles can be estimated based on running the Thermoflow software with a pressure just below critical. STEAM PRO 16 can run at pressures up to 22.0 MPa, and a 1 MPa increase over this value will not result in a very large efficiency increase. Using SoSaT and the PCHE codes, the ultimate turbine inlet temperature can be determined, based on limitations on heat exchanger size which are discussed in Chapter 5. Chapter 5 details the calculation of cycle efficiencies for a wide range of balance of plant configurations. 102

103 4.7 Chapter Summary The development of Fortran codes for heat exchanger modeling has been a major task in examining the possible range of efficiencies for SFRs. These codes have been expanded to include new capabilities needed for modeling different SFR design configurations. Coupled with CYCLES III and STEAM PRO 16, the heat exchanger codes can be used to determine the achievable efficiency of an SFR. Printed Circuit Heat Exchanger (PCHE) codes have been expanded to include sodium-to-sodium and sodium-to-water heat exchangers. They are compact and highly effective. The SoSaT code was written from scratch to model shell-and-tube heat exchangers. It performs calculations for sodium-to-sodium, sodium-to-co 2, and sodium-towater heat exchangers. Water can be either boiling or supercritical. Tubes can be single or double-walled and can include enhanced heat transfer surfaces for CO 2. Baffles can be included on the shell side. Eliminating the intermediate loop is only a practical option for loop-type SFR designs. This idea is elaborated in Chapter 5. Using an alternate fluid in the intermediate loop was shown by Cooper and Lee to have no advantage for any of the fluids studied. Most efficiency gains therefore, will come from measures to raise the average core outlet temperature or changes in the balance of plant. The tools developed here are used in Chapter 5 to quantify the achievable efficiency of an SFR and to compare the performance of heat exchangers and power cycles from an efficiency perspective. In Chapter 5, the range of options for SFR design will be discussed and results from the heat exchanger codes will be used to show the achievable efficiencies of SFRs. 103

104 4.8 Nomenclature for Chapter 4 A flow area or heat transfer area (m 2 ) c p specific heat at constant pressure (J/kgK) d tube or channel diameter (m) D shell diameter (m) e height of axial ribs in enhanced tubes (m) f friction factor g acceleration due to gravity (9.80 m/s 2 ) G mass flux (kg/m 2 s) h heat transfer coefficient (W/m 2 K) h enthalpy (J/kg) J adjustment factor for the Bell-Delaware method (dimensionless) K form loss coefficient k thermal conductivity (W/mK) L length (m) m N Nu NTU P w p Q mass flow rate (kg/s) integer number of tubes, ribs, channels, etc. Nusselt number Number of Transfer Units Wetted Perimeter (m) Pressure (Pa) thermal power (W) q heat flux (W/m 2 ) q linear heat rate (W/m) Re Reynolds number T Temperature ( o C) U Overall heat transfer coefficient (W/m 2 K) v velocity (m/s) W work (W) x equilibrium steam quality Greek Letters ε η μ ρ ζ Effectiveness efficiency viscosity (Pa s) Density Liquid surface tension 104

105 Subscripts b c f fin g i in l lo Na o out r s baffle bundle bypass flow baffle cut liquid characteristic of the tube enhanced surface vapor inside dimension Inlet condition baffle leakage liquid only Sodium property outside dimension Outlet condition baffle temperature gradient baffle spacing 105

106 5 Increasing the Efficiency of the SFR 5.1 Introduction As stated in Chapter 4, increasing average core outlet temperature, improving heat transfer to the PCS, and improving PCS performance are likely to produce the greatest efficiency increases for an SFR. Previous research has indicated that several methods of increasing average core outlet temperature can be employed in the SFR. It is feasible that SFR core outlet temperatures can be up to 575 o C, as in the BN-1800 design [IAEA, 2006]. With such high temperatures, and effective heat transfer to the PCS, efficiencies can be very high indeed. Determining the efficiency benefit of these temperature increases will allow financial considerations to take their long term effect into account more accurately. The tools developed in this research and described in Chapter 4 allow a comparison between different heat exchanger options. CYCLES III and STEAM PRO 16 allow for a comparison between the S-CO 2 recompression cycle and the traditional Rankine cycle. All of these tools combined produce a wide range of BOP options that can be considered. A small increase in plant efficiency could result in very large economic benefits, and therefore a difference of less than 1% in efficiency may be economically significant. 5.2 A Reference Design: The ABR-1000 In order to make meaningful comparisons of design options, a reference design is required. The ABR-1000 is a concept reactor designed by Argonne National Laboratory [Grandy and Seidensticker, 2007]. It is a four-loop, pool type, 1000 MWth reactor with a high pressure traditional Rankine PCS. The ABR-1000 design reports that the PCS achieves a thermal efficiency of 38 % with a steam temperature of 454 o C and a pressure of 15.5 MPa at the turbine inlet. Comparisons will be made with this reference design in regard to heat exchanger options, the effect of increased core outlet temperature, and the choice of PCS. For ease of comparison, the steam generator for the reference temperature and flow rate conditions was assumed to be a straight shell-and-tube heat exchanger that matched the reference design in flow rates, temperatures, and overall heat transfer area. This approach was taken because heat transfer coefficients will not vary appreciably between a helical coil steam generator and a straight tube steam generator, and SoSaT has been written for straight tubes. Both straight tube and helical coil steam generators are considered the best options for SFRs of the future and both have been included in SFR designs [IAEA, 2006], [Chikazawa et al., 2008]. The ABR-1000 steam generator has a helical coil bundle height of 11.6 m and this dimension was preserved in the comparisons performed. The heat transfer in a straight-tube steam generator of 11.6 m in height is much better than that of a helical coil steam generator of 11.6 m 106

107 because the number of tubes is much larger in a straight tube steam generator. For example, the total heat transfer area of the ABR-1000 helical coil steam generator is 1806 m 2, as compared to a heat transfer surface of ~5000 m 2 for a straight tube design with equal shell dimensions. The additional heat transfer area makes a marked difference. The ABR-1000 steam generator achieves a steam temperature of 454 o C at outlet, while an 11.6 m tall straight tube steam generator achieves a steam temperature of 486 o C. This translates to an efficiency gain of 0.8 % in a Rankine cycle. Because the straight-tube steam generator is modeled in SoSaT, it has taken the place of the helical coil steam generator in the reference balance of plant while preserving the shell dimensions. Thus, the efficiency of the reference design is higher than that of the ABR The total heat transfer area of a straight-tube design and a helical coil design will not be very different, but some studies have shown that the reliability of helical coil designs could be significantly higher than that of straight tube steam generators. For example, helical coil designs have not experienced fretting or high cycle fatigue due to the different welds used at the tube sheet [Chikazawa et al., 2008]. For efficiency comparisons, this study only considers straighttube designs, but the helical coil steam generator design could be important for reducing the cost of steam generators. The reference balance of plant is summarized in Table 5.1. Table 5.1: The reference balance of plant Core Outlet Temperature ( o C) 510 Core Thermal Power (MW) 1000 (250 MWth per loop) P-IHX Height (m) 5.20 Shell Diameter (m) 1.72 S-IHX Height (m) 11.6 Shell Diameter (m) 2.81 Steam Pressure (MPa) 15.5 Steam Temperature ( o C) 454 Net Cycle Efficiency (%) 38 Intermediate Pumping Power (MW) ~1.6 (~0.4 MW per loop) Primary Sodium Flow Rate (kg/s) 1256 Intermediate Sodium Flow Rate (kg/s) 1256 Primary Pumping Power (MW) Options for Increasing Core Outlet Temperature Placing ribs, or long, semi-circular protrusions within the hexagonal assembly cans can flatten the temperature profile of the core outlet flow by reducing flow in non-heated edge 107

108 subchannels [Memmott, 2009]. During transients, the peak cladding temperature limit will be met in the hottest channel, but if all the channels are at about the same temperature, the average core outlet temperature can be much higher without increasing the temperature of the hot channel. Thus, the average core outlet temperature can be increased without endangering any margins to the peak clad temperature limit. Because the efficiency of the PCS is driven primarily by temperature, this modification is particularly appealing. RELAP-5 models of the SFR have shown that core outlet temperature profile has a difference of 60 o C for cold assemby dimensions and 30 o C for hot assembly dimensions from the interior to exterior subchannels. With ribs in place, this temperature difference can be reduced to less than ~2 o C [Memmott, 2009]. This result means that the average core outlet temperature could be increased by almost 15 o C from the reference case of 510 o C without endangering any peak temperature limits. This method appears to be the most effective available. Diluent grading in the fuel can flatten the core power profile as well. Power is reduced in the high power region by increasing the fraction of Zr in the fuel, or by placing dummy rods into these regions to flatten the core power profile. This option greatly affects the refueling cycle and will probably produce cycle lengths of too short a period to be economically attractive [Denman, 2009]. The opposite approach is to create enrichment zones in the lower power regions to increase the power there. These and other design options create a range of core outlet temperatures in SFRs. Table 5.2 includes the core outlet temperatures of some power-producing SFRs. The BN-1800 design still requires many decisions to be made about the construction of the core, so the outlet temperature for the BN-1800 reflects an estimate of what the designers believe to be achievable. Table 5.2: Core Outlet Temperatures of Selected SFRs Reactor Core Outlet Temperature ( o C) Super-Phenix 1(France) 545 ALMR (USA) 498 JSFR-1500 (Japan) 550 BN-800 (Russian Federation) 547 BN-1800 (Russian Federation) 575 ABR-1000 (USA) Option Space The option space consists of variation in core outlet temperature, heat exchanger type, elimination of the intermediate loop, and choice of PCS as shown in Figure

109 Figure 5.1: The arrangement of components in the SFR balance of plant and the options available for each component. These choices are summarized in analogy to a fault tree in accident space, as shown in Figure 5.2. The selection of each component will lead to changes in the efficiency of the plant. Figure 5.2: The design choices affecting efficiency that are considered in this study Figure 5.2 is meant to reflect the range of options in developing a balance of plant for an SFR. Core outlet temperature could very well reach up to 575 o C. The primary IHX could be a PCHE or a shell-and-tube design, or the intermediate loop could be eliminated. The secondary IHX could be either PCHE or shell-and-tube, and the PCS could be an S-CO 2, conventional 109